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New traveling waves solutions to generalized Kaup-Kupershmidt and Ito equations. (English) Zbl 1185.35225
Summary: We consider a special fifth-order KdV equation with constant coefficients and we obtain traveling wave solutions for it, using the projective Riccati equation method. By means of scaling, exact solutions to general Kaup-Kupershmidt (KK) equation are obtained. As a particular case, exact solutions to standard KK equation can be derived. Using the same method, we obtain exact solutions to standard Ito equation. By means of scaling, new exact solutions to general Ito equation are formally derived.
35Q53KdV-like (Korteweg-de Vries) equations
35C07Traveling wave solutions of PDE
35A24Methods of ordinary differential equations for PDE
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