×

zbMATH — the first resource for mathematics

Special forms of the fifth-order KdV equation with new periodic and soliton solutions. (English) Zbl 1122.65393
Summary: We consider two special forms of the fifth-order Korteweg-de Vries (KdV) equation that are of particular significance: the Lax and Sawada-Koterra equations. Using a generalization of extended tanh method, new periodic and soliton solutions for this equations are formally obtained.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hirota, R., Direct methods in soliton theory, (1980), Springer Berlin
[2] Ablowitz, M.J.; Clarkson, P.A., Soliton, nonlinear evolution equations and inverse scattering, (1991), Cambridge University Press New York · Zbl 0762.35001
[3] Baldwin, D.; Goktas, U.; Hereman, W.; Hong, L.; Martino, R.S.; Miller, J.C., Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear pdfs, J. symbolic comput., 37, 6, 669-705, (2004), Preprint version available from: nlin.SI/0201008(arXiv.org) · Zbl 1137.35324
[4] Fan, E., Extended tanh-function method and its applications to nonlinear equations, Phys. lett. A, 227, 212-218, (2000) · Zbl 1167.35331
[5] Conte, R.; Musette, M., Link between solitary waves and projective Riccati equations, J. phys. A math., 25, 5609-5623, (1992) · Zbl 0782.35065
[6] Yan, Z., The Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear differential equation, Comput. phys. commun., 152, 1, 1-8, (2003), Preprint version available from: · Zbl 1196.35068
[7] Olver, P.J., Applications of Lie group to differential equations, (1980), Springer-Verlag
[8] A.M. Wazwaz, The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.07.002. · Zbl 1115.65106
[9] Lax, P.D., Integrals of nonlinear equations of evolution and solitary waves, Commun. pure appl. math., 62, 467-490, (1968) · Zbl 0162.41103
[10] Sawada, K.; Kotera, T., A method for finding N-soliton solutions for the KdV equation and KdV-like equation, Prog. theory. phys., 51, 1355-1367, (1974) · Zbl 1125.35400
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.