This is a very interesting question with many possible answers.   In addition to helpful answers already given, there is a bit more to consider.

Wave theory and economics have something in common, namely, mathematics. especially in numerical simulations of linear and non-linear phenomena.   To see what I mean, take a look at Section 3.1, starting on page 42 in

https://www.utwente.nl/ewi/aa/people/phd%20Alumni/thesis/thesis-jaapharmwesthuis.pdf

Wave theory is useful in studying the cyclic behavior of economies and economic variables as well as in the study of economic system dynamics.    For more about this, see, for example, Section 2.1 in

file:///Users/jfpeters/Downloads/EPS2006091MKT9058921239DEGROOT.pdf

See, also:https://www.researchgate.net/profile/Amitava_Chatterjee4/publication/266476679_The_Application_of_Fibonacci_Sequence_and_Elliot_Wave_Theory_in_Predicting_Security_Price_Movements_A_Survey/links/5587f25808aef58c03a07a95.pdf?origin=publication_list

More to the point, my own view is that wave theorists could look forward to a promising second career in economics, provided the aspects of economics considered have strong connections with the characteristics of dynamical systems, especially in considering the behaviour of physical wave phenomena.

Article The Application of Fibonacci Sequence and Elliot Wave Theory...

I don't see any difficulty in another career option, if there exists a passion towards it.

The future is evolving towards multi discipline, hence inter disciplinary career will be more opted.

The rise in interdisciplinary programs is presenting some new challenges for scholars. Your ability to demonstrate that you’re the perfect fit for a position can be a complex process in an interdisciplinary job market, so we have turned to people on both sides of the process – job seekers and faculty with experience on hiring committees – to discover what strategies are most effective in landing an academic position in an institution where the disciplinary boundaries are blurred.

Refer - University affairs

http://www.universityaffairs.ca/career-advice/career-advice-article/how-to-shine-in-an-interdisciplinary-job-market/

Thank you for your opinion, Krishnan! Indeed, I also think that future science will be more interdisciplinary. However, the difficulty to combine two sciences varies across the set of pairs. For example, statisticians are very welcome to economics, and they also do not need to study a lot of new issues. Econometrics is just a subset of statistics. My experience is that it is much  more difficult for wave theorists to bring some elements of their knowledge to economic science. The question is: why?

Dear Yuri Yegorov, 

I think that for the specialist in wave theory it is possible to do a second career in economics!

A career in the economics in the world (especially in Russia) do not only experts in wave theory, but experts on scientific communism, atheism, astrology, homeopathy (and other pseudoscience), and - not experts, people without higher education!  Joke!

And now I'm serious: "Wave theory is described by partial differential equations involving typically space and time as continuous variables". Because a specialist in wave theory can be an excellent economist!

Dear Prof. Zabrodskij, thank you for answering this question! I think that in Russia everything is possible. I was at several economic conferences there, and found that people are very tolerant to different paradigms and schools. Mathematical knowledge of any sort is also welcome because Marxism (the only economic knowledge studied in Russia before 1990) was non-mathematical, while neoclassical economics (that dominates today both in Western economic schools and Russia) is rather mathematical. But my experience is that in the West it is very different.

Because economists like to have economists around. I have the same problem as a forester that did a lot of modelling and statistics, and a thesis on economics. One of the difficulties is, that everybody that isn't from economics is a bigger wager than the tons of guys that studied in economy-related fields. On the other hand, economists can hold introductory courses in economy that I couldn't handle without a lot of preparation. Quality would be higher, though ;-)

This is a very interesting question with many possible answers.   In addition to helpful answers already given, there is a bit more to consider.

Wave theory and economics have something in common, namely, mathematics. especially in numerical simulations of linear and non-linear phenomena.   To see what I mean, take a look at Section 3.1, starting on page 42 in

https://www.utwente.nl/ewi/aa/people/phd%20Alumni/thesis/thesis-jaapharmwesthuis.pdf

Wave theory is useful in studying the cyclic behavior of economies and economic variables as well as in the study of economic system dynamics.    For more about this, see, for example, Section 2.1 in

file:///Users/jfpeters/Downloads/EPS2006091MKT9058921239DEGROOT.pdf

See, also:https://www.researchgate.net/profile/Amitava_Chatterjee4/publication/266476679_The_Application_of_Fibonacci_Sequence_and_Elliot_Wave_Theory_in_Predicting_Security_Price_Movements_A_Survey/links/5587f25808aef58c03a07a95.pdf?origin=publication_list

More to the point, my own view is that wave theorists could look forward to a promising second career in economics, provided the aspects of economics considered have strong connections with the characteristics of dynamical systems, especially in considering the behaviour of physical wave phenomena.

Article The Application of Fibonacci Sequence and Elliot Wave Theory...

Nothing is impossible for who has faith.

Dear Yuri Yegorov,

I fully agree with you!

Dear Artur, Klemens, James and Mariano, thank you very much for the contribution to this discussion. In the next message I will try to elaborate on some of your ideas.

Dear Mariano, you are right that all is possible for a man with faith who has some goals. The question is how easy is that. One can teach an elephant to dance but the return to such investment is much lower than for other animals. Every science has its own peculiarities, and correlation between typical assumptions in different sciences can be positive or negative.

Dear Artur, this question was not much for job search in economics by a specialist in wave motion. I agree that there is competition with young who have just got Ph.D. in economics, and the merits in research of wave motion are not likely to be taken into account. I was talking about a specialist in wave motion and PDE, who also has listened to basic economic lectures and tries to promote ideas that are TYPICAL for wave modelling in economic science. In particular, are his/her models likely to be understood and easily published?

Dear Klemens, I think that economics of forest is a potentially good application for wave theorists. Optimal harvesting of forest includes waves, because each tree is growing continuously and has its life cycle. Both space (location of a tree) and time are important variables. There is also age, another continuous variable. Can you tell how the research of wave theorists is accepted among economists who deal with forest?

Dear James, thanks a lot for giving a profound answer including citation. Indeed financial economics is a field where some PDE are applied (like diffusion of future prices in the state space driven by random walk). Your example of Fibonnaci numbers in long term price motion is also interesting. However, those waves are discrete and not described by PDE.

As for your book in hydrodynamics, I am pretty aware of those methods. But can they be applied directly to macroeconomics? Tsunami wave (I also worked on that) can cross the Pacific ocean without losing its energy and (in the case of a soliton) even preserving its shape. If we look at business cycle pattern, we can see that intervals between crises are not so regular.

I have also observed that very few economists can work with time and space simultaneously (and almost nobody when they are both continuous, which is crucial for PDE), and it is difficult to sell such models to journals. Also it is difficult to satisfy standard assumptions about rationality (knowing all leads to rapid change of pattern in time, contrary to slow evolution in wave models).

Those who are interesting in the technology of derivation of PDE for economics in continuous space and time can have a look at my paper: https://www.researchgate.net/publication/279537697_Spatial_Price_Dynamics  . It was presented twice, but I did not elaborate because economists seem to have little interest in such models. However, new equations (not known in physics) might emerge.

 A much less elaborated case about PDE for evolution of population density and wage pattern (with some ideas for applied mathematicians) is shown here: https://www.researchgate.net/publication/305661583_Waves_of_Wages_House_Prices_and_Population_Density

Conference Paper Spatial Price Dynamics

Research Waves of Wages, House Prices and Population Density

Yuri, I think you missed my point. That is: It is difficult for any non-standard-enonomist to change his career path to economics. There is a tendency in economics to dismiss non-economists, regardless of their knowledge and skillset. I argue that this glass-wall blocks even forest ecnomists from being taken seriously. (To quote a professor: "If you want to go into economics, start over and study economics. It's the fastest way. I have struggled 20 years to become accepted.")

To answer your question: In forestry, we usually model the ecosystem much more detailed and not in wave-patterns. Circular, yes, sometimes. Not waves. Maybe if you look into datasets over hundreds of years, but even then we tend to explain it with continuous, one directional processes. Look into the introduction of Hans Pretsch's "Forest dynamics, growth and yield" to gain an impression of what influences forest growth from our perspective. Space becomes almost n-dimensional. trees grow continuously, but their height and girth growth follow different functions. Undisturbed, forests on a somewhat large scale will have a steady state, with more chaotic patterns in smaller scales. Most tree species are able to inhibit their growth in their youth, if the resource situation is not favourable, but show atypical fast growth in higher ages, when the situation improves.

Single trees are dependent on dozens of resources, including light and temperature. They can get infected or destroyed by animals. Singlular extreme weather events can kill them. Put together in a forest, they compete with each other.

Plantations on more or less homogenous ground can maybe dealt with using wave patterns. But even then, it would probably more look like a tan-function.

Dear Klemens, I think that we understand each other, and now you have purified your statement. So you are talking about some artificial barrier created by economists to prevent an entry to their camp from outside. (Like in incumbent-entrant game in industrial organization). I know both camps and I have 2 Ph.D.

I do not want to focus on extra complexity and dimensionality of forest models (that you are talking) simply because this should favor (rather than close) a possibility to use wave-theoretical approach in some cases.

A new statement for me is that forest economics is not much different from other economics. I thought differently. In forest and agricultural economics a researcher has to take into account land explicitly, because neither product can grow without it, while soil and weather (both location specific) are important components of production function in both cases. It goes without saying that time is also important here (just because state of plants and their value change continuously with it). So a priori both components for writing PDE (continuous time & space) are not neglected.

Here I want to make extra reference to the new book of Brian Czech (2013): https://www.amazon.com/Supply-Shock-Economic-Crossroads-Solution/dp/0865717443 . Apart from telling us about modern environmental problems and the ways to deal with them, it reveals why land was not included as an input in production function in macroeconomic models, at least in the 20th century (before it was).

Now please have a look at the classical micro-economic textbook for students (by H.Varian; I guess that almost all economic students have to read it); here is free access: http://mileslight.com/armenia/Varian-MicroeconomicAnalysis.pdf . Note that time is not mentioned before chapter 19, and even then just in discrete form. Space is not mentioned at all. This means that most of people with economic education are happy to live in the world without space and time. (Note that for a physicist the world cannot exist without them, because they are essential attributes of matter). Only a minority (those who work in regional science and maybe agricultural economics) know about space. A bit more know about time, more often in a discrete framework (just to be able to run a regression or solve a game by backward induction), while economic growth models are also in continuous time. However, I guess that less than 1% use both space and time, and even less do it in continuous form. So how many will understand a wave theorist who has passed economic courses and now tells about PDE with economic applications? Will this article be published, even if it is fully innovative? Most likely not. Even if all assumptions about rationality are satisfied and there are no mathematical errors, an editor can simply write: "This is not interesting for our readers". I guess that this never happens in journals for applied mathematics.

Dmitry, if you study the sequence of my publications, you will find that I worked with PDE before working in economics and that I have more research in economics now. This question is philosophical and is not linked to my career. As for higher demand and better pay - there are also waves. In the moment (1990s) when I started to study and then to work in economics, there was a huge negative global shock in both demand and pay for all physicists, including wave theorists. (By the way, you are Doctor in philosophy who works not in this area but in computations). You might have an interest to look at my paper about dynamics of research and optimal behaviour, even cascade effect is discovered here (all modelling is based on economic principles, but broader math tools are used): https://www.researchgate.net/publication/272349207_The_Dynamics_of_Research_Schools_and_the_Demand_for_Teaching

P.S. An interesting comment about demand for different skills in math:

“Probability. A strong background in probability will permit to qualify for jobs in statistics and financial math. See AMS Notices where a lot of statistics about the employment of recent PhD is published yearly. And a salary survey.

My second guess was combinatorics/coding theory or PDE. But my friend explained me that PURE combinatorics is not so hot in the (industrial) job market, coding theory is not pure math, and pure PDE is very different from numerical PDE, the last thing is of course in great demand.”

Source: http://mathoverflow.net/questions/162125/what-areas-of-pure-mathematics-research-are-best-for-a-post-phd-transition-to-in

Conference Paper The Dynamics of Research Schools and the Demand for Teaching

Dear Yuri,

Thanks you inviting me to participate in the discussion.

The notion of ‘follow your dream’ is a wonderful sentiment, but one has to have a clear-eyed vision of what he/she bring out of the new venture. Both wave theory and economics have mathematics in common. One of the most prominent economic cycle theories is known as "the Kondratieff wave". The Elliott wave theory forecasts stock market prices by charting their movements through regular cycles.Economy move in predictable waves, cycles or patterns theories have enabled some analysts to correctly predict the timing of recessions, stock market peaks and stock market crashes over the past couple of decades. A wave theory expert can go for a second career in economics if he/she holds the passion for the same and has adequate knowledge and aptitude to recognize and capitalize on his/her transferable skills.

Dmitry, can you please use less abbreviations; they are clear only for narrow field specialists. EM is probably electro-magnetic, but only for those who know only physics. Is RF = Russian Federation?

As for me, I am not  a programmer. I am a theorist, mathematical modeller, both with application in natural and social sciences. I put my papers online on RG. The most inter-disciplinary is perhaps this: https://www.researchgate.net/publication/271500062_Econo-physics_A_Perspective_of_Matching_Two_Sciences

Article Econo-physics: A Perspective of Matching Two Sciences

Great question. I'd say the answer is more cultural than it is logical or justifiable.

My experience with economics is as a student taking economics elective courses. The math, as others have said, is much the same as in electrical engineering, but what math is used tends to terrify the students. I got the impression that economists, for the most part, do not appreciate the convergence of these disciplines. And yet, there are rays of hope. Did you see this, for instance?

http://www3.imperial.ac.uk/pls/portallive/docs/1/40346.PDF

I'm no doubt biased. My observation is that non-engineers do not understand engineering remotely well enough to see how it might relate to their discipline. The parallels, the similarity of the math, do not strike them. (This applies to statistics too, biology, and other fields, for that matter.) So when attempting to enter that culture from engineering or physics, one is met with skepticism. What does he know?

Perhaps a few well-placed papers, such as the one in the link, can begin to bridge the gap.

Dear Yurii, I've studied so many areas in mathematics, mathematical physics and mathematical modeling that I think I can apply my skills to economics as well. Moreover,  I was teaching mathematical modeling in international economics at a University  at some point. Do you have statistics specific to wave theorists?

May be its a good choice, as physics and economics have WAVE FUNCTION

https://orderstatistic.wordpress.com/2014/03/21/why-are-physicists-drawn-to-economics/

Nice ideas. I would like just to give a more historic perspective. The mathematics were not always married with physics or engineering. The marriage was achieved by Newton, along with his calculus (and Leibniz). I argue it would be needed another huge step in mathematics, like that of Newton, from a perhaps so influential scientist, in order to marriage again such different fields, Mathematics/Engineering with Economics. The mathematical tools of today with the PDE are just not enouph to model such natural systems as economy. Also let us not forget that PDEs did not get created to model such systems. Newton and his colleagues, Euler, Laplace, Lagrnage, Stokes, D' Alambert, etc i believe had more natural problems in mind, than to model the movement of economy. Finally this opinion is not mine, but comes from J.v. Newman, one from the best mathematicians of the previous century, who also wrote a good paper in economy-mathematics. One same 'soon to be marriage,' can be noticed between medicine and mathematics where the progress is already good. I am referring to bio-egnineering fields which are generally in growth. But still if you go to a doctor, he will not analyze your temperature field of your body or calculate the mean velocity of the blood with Matlab. The time is just not ready yet to ripe those 'Fruits of science' . One needs patience and to want it badly enouph.

Sorry for the spelling errors, John von Neumann

https://en.wikipedia.org/wiki/John_von_Neumann#Mathematical_economics

Dear Albert, thanks you for the interesting comment. I agree that finance is using more engineering skills, and that some people with technical and physical background come there. Fourier transform is a great instrument but it is practically unused in economics. Even standard tools of econometric programs do not have it, just linear regression. I also think that its power in finance is lower, because a signal has a faster time of decay. I guess that some equations of statistical physics can be powerful here. But we will not find this in financial publications that are more about equilibrium existence. If a former physicist manages to find an algorithm that can suggest a good prediction for future price trend, it will remain secret and enter some trading program which will cost a lot. That is just my opinion, I do not know all literature.

Dear Gryllakis and Krishnan! A lot of thanks for contribution to this discussion.

Dear Natalia, thank you for sharing your experience. I know that mathematicians from outside economics can teach special curses, like math for economists or statistics for economists.

I was also sure (in early 1990s) that with my Ph.D in mathematical physics I will easily write another one in economics and will use there part of my previous knowledge. This did not work; my economic Ph.D. satisfies all economic standards, although I kept there spatial variable (but not time). I understood well before the defense that PDE will not help me to defend thesis (the reasons are explained above and not only in my comments).

I still think that elements of knowledge from physics can help to understand better some economic phenomena, and thus I continue to work also in intersection between economics and physics. But I would never have economic publications if I would persist to put physical ideas in all of my papers.

My motivation to raise this question was in conversation with a student who asked similar question and where I gave my experience: https://www.researchgate.net/post/Financial_Application_of_Wave_Equations_Burger_KdV_Schrodinger_etc

Those who have a large base culture in physics or mathematics are generally accustomed to working on complex and complicated systems. The complex systems are unpredictable; that is, the same sequence of actions does not always lead to the same solution even if there is always a certain probability, sometimes calculable, to find the same solution. The complicated systems are predictable ie no matter how large is the number of actions to be performed on the system, the end you always find the same solution. The economy, mainly,  is a complex system and sometimes also complicated. Consequently, a specialist in wave theory can surely be successful in economics.

Dear Leonardo, there is a difference between “being useful objectively” and “being able to make a career”. There is no doubt that a set of fresh ideas from other science can often fertilize another science. But will it be accepted? Not the God judges a scientist, but his peer. Sometimes not by the public vote (like on RG), but only from those in powerful position. I just tried to explain the evidence why not all ideas from wave theory are welcome by economists. Partly because the education in the field is such that this knowledge is not given. And when people do not understand something, they fear and reject it. This is also a robust strategy, because otherwise many false scientists will come and spoil it.

I am not referring to a series of new ideas from a science which can fertilize another science. But I speak of the "forma mentis" that physicists and mathematicians have acquired during their studies or works. This mindset works very well to find the best solutions to many economic problems. This same mentality does not work very well in other areas such as for example policy.