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Two applications of the homogeneous balance method for solving the generalized Hirota-Satsuma coupled KdV system with variable coefficients. (English) Zbl 1170.35519
Summary: The homogeneous balance method is used to search for Bäcklund transformation and similarity reductions of the generalized Hirota-Satsuma coupled KdV system with variable coefficients. New solitary wave solutions and two similarity reductions are obtained. The nonlinear system is reduced to two systems of ordinary differential equations and the first one is solved by using the F-expansion method. New exact solutions on the form of Jacobi elliptic functions, hyperbolic and periodic functions are obtained.
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
37K35Lie-Bäcklund and other transformations
35B10Periodic solutions of PDE
35C05Solutions of PDE in closed form
35A30Geometric theory for PDE, characteristics, transformations