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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.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35B10 Periodic solutions to PDEs
35C05 Solutions to PDEs in closed form
35A30 Geometric theory, characteristics, transformations in context of PDEs
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