Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. (English) Zbl 1125.35401

Summary: The solitary wave solutions of the approximate equations for long water waves, the coupled KdV equations and the dispersive long wave equations in \(2 + 1\) dimensions are constructed by using a homogeneous balance method.


35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35A35 Theoretical approximation in context of PDEs
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