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Zbl 1170.35519
Moussa, M.H.M.; El Shikh, Rehab M.
Two applications of the homogeneous balance method for solving the generalized Hirota-Satsuma coupled KdV system with variable coefficients. (English)
[J] Int. J. Nonlinear Sci. 7, No. 1, 29-38 (2009). ISSN 1749-3889; ISSN 1749-3897/e

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 2000:: *35Q53 KdV-like equations
35Q51 Solitons
37K35 Lie-Bäcklund and other transformations
35B10 Periodic solutions of PDE
35C05 Solutions of PDE in closed form
35A30 Geometric theory for PDE, transformations

Keywords: generalized Hirota-Satsuma coupled KdV system; variable coefficients; homogeneous balance method; auto-Bäcklund transformations; direct method; $F$-expansion method; solitary wave solution

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Zentralblatt MATH Berlin [Germany]