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Higher-order equations of the KdV type are integrable. (English) Zbl 1206.35220
Summary: We show that a nonlinear equation that represents third-order approximation of long wavelength, small amplitude waves of inviscid and incompressible fluids is integrable for a particular choice of its parameters, since in this case it is equivalent to an integrable equation which has recently appeared in the literature. We also discuss the integrability of both second- and third-order approximations of additional cases.

35Q53KdV-like (Korteweg-de Vries) equations
35Q35PDEs in connection with fluid mechanics
37K05Hamiltonian structures, symmetries, variational principles, conservation laws
Full Text: DOI EuDML
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