Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. (English) Zbl 0972.35062

Summary: A Jacobi elliptic function expansion method, which is more general than the hyperbolic tangent function expansion method, is proposed to construct the exact periodic solutions of nonlinear wave equations. It is shown that the periodic solutions obtained by this method include some shock wave solutions and solitary wave solutions.


35L05 Wave equation
35L70 Second-order nonlinear hyperbolic equations
35A08 Fundamental solutions to PDEs
Full Text: DOI


[1] Wang, M. L., Phys. Lett. A, 199, 169 (1995)
[2] Wang, M. L.; Zhou, Y. B.; Li, Z. B., Phys. Lett. A, 216, 1, 67 (1996)
[3] Yang, L.; Zhu, Z.; Wang, Y., Phys. Lett. A, 260, 55 (1999)
[4] Yang, L.; Liu, J.; Yang, K., Phys. Lett. A, 278, 267 (2001)
[5] Parkes, E. J.; Duffy, B. R., Phys. Lett. A, 229, 217 (1997) · Zbl 1043.35521
[6] Fan, E., Phys. Lett. A, 277, 212 (2000)
[7] Hirota, R., J. Math. Phys., 14, 810 (1973)
[8] Kudryashov, N. A., Phys. Lett. A, 147, 5-6, 287 (1990)
[9] Otwinowski, M.; Paul, R.; Laidlaw, W. G., Phys. Lett. A, 128, 483 (1988)
[10] Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q., Appl. Math. Mech., 22, 326 (2001)
[11] Yan, C., Phys. Lett. A, 224, 77 (1996)
[12] Porubov, A. V., Phys. Lett. A, 221, 391 (1996)
[13] Porubov, A. V.; Velarde, M. G., J. Math. Phys., 40, 884 (1999)
[14] Porubov, A. V.; Parker, D. F., Wave Motion, 29, 97 (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.