Weierstrass semi-rational expansion method and new doubly periodic solutions of the generalized Hirota-Satsuma coupled KdV system. (English) Zbl 1094.65104

Chen, Yong; Yan, Zhenya

Appl. Math. Comput. 177, No. 1, 85-91 (2006).

Summary: With the aid of symbolic computation, we investigate the generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) system via our Weierstrass semi-rational expansion method presented recently using the rational expansion of Weierstrass elliptic function and its first-order derivative. As a consequence, three families of new Weierstrass elliptic function solutions via Weierstrass elliptic function \(\wp(\xi;g_2,g_3)\) and its first-order derivative \(\wp'(\zeta;g_2,g_3)\). Moreover, the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented, and when \(\zeta\to \infty\), these solitary wave solutions approach to some constants.

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53	KdV equations (Korteweg-de Vries equations)
35Q51	Soliton equations

Keywords:

symbolic computation; Hirota-Satsuma coupled Korteweg-de Vries (KdV) system; Weierstrass semi-rational expansion method; Weierstrass elliptic function; Jacobi elliptic function; solitary wave solutions

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