Abstract:
A fifth-order nonlinear partial differential equation for the description of nonlinear waves in a liquid with gas bubbles is considered. Special solutions of this equation are studied. Some elliptic and simple periodic traveling wave solutions are constructed. Connection of selfsimilar solutions with Painlevé transcendents and their high-order analogs is discussed.
Keywords:waves in a liquid with gas bubbles, evolution equations, exact solutions, meromorphic solutions, fifth-order KdV equation, Kaup–Kupershmidt equation.
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