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) Zbl 1170.35519 Int. J. Nonlinear Sci. 7, No. 1, 29-38 (2009). 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. Cited in 5 Documents 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 Keywords:generalized Hirota-Satsuma coupled KdV system; variable coefficients; homogeneous balance method; auto-Bäcklund transformations; direct method; \(F\)-expansion method; solitary wave solution PDFBibTeX XMLCite \textit{M. H. M. Moussa} and \textit{R. M. El Shikh}, Int. J. Nonlinear Sci. 7, No. 1, 29--38 (2009; Zbl 1170.35519)