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

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.


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
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[1] Ablowitz, M. J.; Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0762.35001
[2] Satsuma, J.; Hirota, R., J. Phys. Soc. Jpn., 51, 3390 (1982)
[3] Hirota, R.; Satsuma, J., Phys. Lett. A, 50, 407 (1981)
[4] Tam, H. W., J. Phys. Soc. Jpn., 68, 369 (1999)
[5] Yan, Z. Y., Chaos, Soliton & Fractals, 15, 575 (2003)
[6] Yan, Z. Y., Comput. Phys. Commun., 148, 30 (2002)
[7] Yan, Z. Y., Commun. Theor. Phys., 43, 391 (2005)
[8] Porubov, A. V.; Velarde, M. G., J. Math. Phys., 40, 884 (1999)
[9] Yan, Z. Y., Z. Naturforsch. A, 59, 29 (2004)
[10] Patrick, D. V., Elliptic Function and Elliptic Curves (1973), Cambridge University Press: Cambridge University Press Cambridge
[11] Lawden, D. F., Elliptic Functions and Applications (1989), Springer-Verlag: Springer-Verlag New York · Zbl 0562.53046
[12] Hon, Y. C.; Fan, E., Appl. Math. Comput., 146, 813 (2003)
[13] Fan, E., Phys. Lett. A, 282, 18 (2001)
[14] Chen, Y., Chin. Phys., 12, 1 (2003)
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