14 Questions 73 Answers 0 Followers
Questions related from R. Mark Bradley
We are studying a system of the form dx/dt = A(t) x, where x(t) is a two-component column vector and A(t) is a 2x2 matrix with the property A(t + \tau) = A(t) for all t. Floquet theory can be...
07 July 2014 5,504 10 View
I imagine that experts in the field will find this question trivial, but I'm not one of the cognescenti. Thanks in advance for your help.
06 June 2014 3,186 8 View
I would like to find the exact solution to the system dA/dt = B - ikv cos(wt) A dB/dt = -B - ik cos(wt) A, where A=A(t) and B=B(t) are complex and v, k and w are real constants. Got any ideas?
06 June 2014 4,976 31 View
Is anyone familiar with a version of time-dependent perturbation theory in which both the unperturbed Hamiltonian and the perturbation are not Hermitian? The unperturbed Hamiltonian is constant...
06 June 2014 5,570 7 View
Consider the boundary value problem \sqrt(y)(1 + cy'') = x(x^2-1) with boundary conditions y(1) = y(-1) = 0. Here y = y(x), the primes denote derivatives with respect to x, and c is a positive...
03 March 2014 9,539 7 View
Can anyone suggest an analytical method to solve the ODE a^2 y = y^3 - y''' - y', where a is a positive constant? The solution should have y(0) = 0. Also y -> a and y' -> 0 as x -> infinity.
11 November 2013 940 63 View
Can anyone suggest a method to solve the nonlinear diffusion equation u_t = -u_xxxx + (u^2)_xx subject to the initial condition u(x,0)=delta(x) and the boundary conditions u, u_x -> 0 as x ->...
11 November 2013 5,612 9 View
I learned to my surprise from an earlier question that there are special cases in which two nontrivial solutions to a nonlinear ODE add to give a new nontrivial solution. (See "Does this ODE have...
11 November 2013 7,639 3 View
Does the nonautonomous nonlinear ODE [y''' - (y')^2 + xy]' = 0 have a nonzero solution that is bounded everywhere? If there is a solution, can it be found in analytical form? Note that there is...
11 November 2013 9,962 13 View
The system of equations u_t + (\partial_x^2 + \partial_y^2)u_x + u u_x/2 = -(p_x u_x + p_y u_y)/2 (Eq. 1) p_xx + p_yy = u_x (Eq. 2) reduces to the KdV equation if u and p are independent of...
11 November 2013 9,178 2 View
Is there a way to see intuitively and physically why under-compressive shocks form? The formation of compressive (Lax) shocks makes perfect sense to me, but I can't see why under-compressive...
11 November 2013 1,111 6 View
Can anyone suggest an analytical method to solve y^3 + y''' = 0? The solution should satisfy the boundary conditions y tends to plus or minus one as x tends to plus or minus infinity. The...
10 October 2013 5,873 39 View
What does it mean if a solution to a PDE is "spectrally stable"?
10 October 2013 5,343 4 View
The Kuramoto-Sivashinsky equation is ut = -uxx - uxxxx + lambda (ux)2, where lambda is a constant and u = u(x,t). It is a paradigmatic partial differential equation that exhibits spatio-temporal...
01 January 1970 882 4 View
