New exact Jacobi elliptic functions solutions for the generalized coupled Hirota–Satsuma KdV system

• Published in: Applied mathematics and computation Vol. 217; no. 2; pp. 472 - 479
• Main Author: Hong, Baojian
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.09.2010; Elsevier
• Subjects: Computation; Construction; Elliptic functions; Exact sciences and technology; Exact solutions; Functional analysis; Functions of a complex variable; Generalized coupled Hirota–Satsuma KdV system; Generalized Jacobi elliptic functions expansion method; Jacobi elliptic functions solutions; Mathematical analysis; Mathematical models; Mathematics; Nonlinear differential equations; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Solitary waves; Special functions; Generalized Jacobi elliptic functions expansion method; Generalized coupled Hirota–Satsuma KdV system; Jacobi elliptic functions solutions; Exact solutions; Jacobi method; Initial value problem; Generalized coupled Hirota-Satsuma KdV system; Symbolic computation; Periodic solution; Partial differential equation; Exact solution; Non linear equation; Numerical analysis; Boundary value problem; Applied mathematics
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.05.079

In this paper, an generalized Jacobi elliptic functions expansion method with computerized symbolic computation is used for constructing more new exact Jacobi elliptic functions solutions of the generalized coupled Hirota–Satsuma KdV system. As a result, eight families of new doubly periodic solutions are obtained by using this method, some of these solutions are degenerated to solitary wave solutions and triangular functions solutions in the limit cases when the modulus of the Jacobi elliptic functions m → 1 or 0, which shows that the applied method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.