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Travelling wave solutions to some important equations of mathematical physics. (English) Zbl 1237.35028
Summary: Exact travelling wave solutions of some nonlinear evolution equations of mathematical physics are obtained by using the mapping method and the extended \(F\)-expansion method. It is well known that different types of exact solutions of a given auxiliary ordinary differential equation produce new types of exact solutions to nonlinear evolution equations. Many new exact travelling wave solutions of the Zakharov-Kuzentsov (ZK), modified Kadomtsev-Petviashvilli (KP) with square root nonlinearity and modified fifth-order Korteweg-de Vries (KdV) equations are constructed by using the mapping method. We also apply the extended \(F\)-expansion method to the long-short-wave interaction system and the coupled modified KdV equations. The solutions obtained in this paper include single and combined Jacobi elliptic function solutions, rational solutions and hyperbolic function solutions. In the limiting case, the solitary wave solutions of such equations and systems are also studied.

MSC:
35C07 Traveling wave solutions
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35A24 Methods of ordinary differential equations applied to PDEs
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