CH equation is an important model equation in simulating the shallow water problems. as what I have learned, it was mostly derived by the variational method. I want to learn something about it from the primary control equations by using method of perturbations, such as the Gardner-Morikawa transformation method, multi-scale method et.al. Could anyone tell me some informations or references about the derivation of Camassa-Holm equation for shallow water problems by the method of only perturbation expansions or multi-scale expansion method, but not the variational approach?
attaching a few here...including my thesis..
, Global Weak Solutions for a Shallow Water Equation, Indiana Univ. Math.
J. 47 (1998), 1527{1545.
Degasperis A., Holm D., and Hone A., A New Integrable Equation with Peakon
Solutions, Theoret. and Math. Phys. 133 (2002), 1463{1474.
Dullin H., Gottwald G., and Holm D., An Integrable Shallow Water Equation with
Linear and Nonlinear Dispersion, Phys. Rev. Lett. 87 (2001), 194501.
Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent
equations for shallow water waves, Fluid Dynam. Res. 33 (2003), 73{95.
On asymptotically equivalent shallow water wave equations, Phys. D 190
(2004), 1{14.
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1 Recommendation
Hayat Rezgui
École Normale Supérieure de Kouba
Try to see:
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Hayat Rezgui
École Normale Supérieure de Kouba
You can see:
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Hayat Rezgui
École Normale Supérieure de Kouba
Try to see too:
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Ruigang Zhang
Inner Mongolia University
@Vitalii Pertsevyi ，Hayat Rezgui ·Snehanshu Saha
Thankyou so much for your helpful suggestions, i will refer to them.
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Luca Bonaventura
Politecnico di Milano
You may find here
http://www.worldscientific.com/doi/abs/10.1142/S0218202509003474
a non variational derivation of the shallow water equations themselves, whose technique might be useful in achieving your goal.
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Ghassan Fadhil Smaisim
University Of Kufa
Dear Doctor,
You can depends on the answer of Snehanshu Saha
Good luck
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