×

zbMATH — the first resource for mathematics

The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations. (English) Zbl 1118.81480
Summary: The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the \(F\)-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35B10 Periodic solutions to PDEs
35Q51 Soliton equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Davey, A.; Stewartson, K., Proc. R. soc. London A, 338, 101, (1974)
[2] Malomed, B.; Anderson, D.; Lisak, M.; Quiroga-Teixeiro, M.L.; Stenflo, L., Phys. rev. E, 55, 962, (1997)
[3] Remoissenet, M., Waves called solitons, (1996), Springer Berlin · Zbl 0922.35147
[4] Zhou, Y.B.; Wang, M.L.; Wang, Y.M., Phys. lett. A, 308, 31, (2003)
[5] Liu, S.K.; Fu, Z.T.; Liu, S.D.; Zhao, Q., Phys. lett. A, 289, 69, (2001)
[6] Fu, Z.T.; Liu, S.K.; Liu, S.D.; Zhao, Q., Phys. lett. A, 290, 72, (2001)
[7] Liu, S.K.; Fu, Z.T.; Liu, S.D.; Zhao, Q., Acta phys. sinica, 51, 10, (2002)
[8] Liu, S.D.; Fu, Z.T.; Liu, S.K.; Zhao, Q., Acta phys. sinica, 51, 718, (2002)
[9] Parkes, E.J.; Duffy, B.R.; Abott, P.C., Phys. lett. A, 295, 280, (2002)
[10] Wang, M.L., Phys. lett. A, 213, 279, (1996)
[11] Wang, M.L.; Zhou, Y.B.; Li, Z.B., Phys. lett. A, 216, 67, (1996)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.