Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: V. Marinakis
Pages: [317] - [332]
Received Date: July 7, 2010
Submitted by:
In this paper, we study two nonlinear equations that represent second and third order approximation of long wavelength, small amplitude waves of inviscid, and incompressible fluids. We apply a procedure, which is based on the application of hodograph transformations. In this way, we reveal two integrable cases for the third order approximation. The first was recently identified, as been equivalent to an integrable equation recently appeared in the literature, while the second appears to be new. Our study fails to reveal any integrable cases for the second order approximation. We also discuss the existence of additional integrable cases.
partial differential equations, integrable equations, Painlevé analysis, hodograph transformations.
