The Multi-Soliton Solutions to The KdV Equation by Hirota Method
Abstract
The Hirota bilinear method is used to solve the KdV model. As a result, the exact expression of multi-soliton solutions of the KdV equation is obtained.
Keywords
Full Text:
PDFReferences
Parkes, E. J., & Duffy, B. R. (1996). An automated tanh-functionmethod for finding solitary wave solutions to nonlinear evolution equations. Computer Physics Communications, 98(3), 288-300.
Fan, E. (2000). Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277(4-5), 212-218.
Liu, S., Fu, Z., Liu, S., & Zhao, Q. (2001). Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A, 289(1-2), 69-74.
Fu, Z., Liu, S., Liu, S., & Zhao, Q. (2001). New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Physics Letters A, 290(1-2), 72-76.
Wang, M., & Zhou, Y. (2003). The periodic wave solutions for the Klein-Gordon-Schr¨odinger equations. Physics Letters A, 318(1-2), 84-92.3
Zhou, Y., Wang, M., & T. Miao, T. (2004). The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations. Physics Letters A, 323(1-2), 77-88.
Wang, M., & Li, X. (2005). Extended -expansion method and periodic wave solutions for the generalized Zakharov equations. Physics Letters A, 343(1-3), 48-54.
Wang, M., & Li, X. (2005). Applications of -expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos, Solitons and Fractals, 24(5), 1257-1268.
Wazwaz, A.-M. (2003). A study on nonlinear dispersive partial differential equations of compact and noncompact solutions. Applied Mathematics and Computation, 135(2-3), 399-409.
Wazwaz, A.-M. (2003). A construction of compact and noncompact solutions for nonlinear dispersive equations of even order. Applied Mathematics and Computation, 135(2-3), 411-424.
Wang, M. (1995). Solitary wave solutions for variant Boussinesq equations. Physics Letters A, 199(3-4), 169-172.
Wang, M. (1996). Exact solutions for a compound KdV-Burgers equation. Physics Letters A, 213(5-6), 279-287.
Wang, M., Zhou, Y., & Li, Z. B. (1996). Application of a homogeneous balance method to exact solutions of nonlinear evolutionequations in mathematical physics. Physics Letters A, 216, 67-75.
Hirota, R., & Satsuma, J. (1997). Nonlinear evolution equations generated from the Bäcklund transformation for the Boussinesq equa-tion. Prog Theor Phys, 157, 797-807.
Hirota, R. (1971). Exact solution of the KdV equation formultiple collisions of solitons. Phys Rev Lett, 27, 1192-1194.
Hu, X. B., & Clarkson, P. A. (1995). Rational solutions of a differential-difference KdV equation,the Toda equation and the discrete KdV equation. J Phys A: Math Gen, 28, 5009-5016.
Khatera, A. H., Hassanb, M. M., & Temsaha, R. S. (2007). Co-noidal wave solutions for a class of fifth-order KdV equations. Mathematics and Computers in Simulation, 70, 221-226.
Wazwaz, A. M. (2007). Analytic study on the gen-eralized fifth-order KdV equation: New solitons and periodic solutions. Communications in Nonlinear Science and Numerical Simulation, 12, 1172-1180.
DOI: http://dx.doi.org/10.3968/6902
DOI (PDF): http://dx.doi.org/10.3968/pdf_16
Refbacks
- There are currently no refbacks.
Copyright (c)
Reminder
If you have already registered in Journal A and plan to submit article(s) to Journal B, please click the "CATEGORIES", or "JOURNALS A-Z" on the right side of the "HOME".
We only use the follwoing mailboxes to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
[email protected]
[email protected]
Articles published in Progress in Applied Mathematics are licensed under Creative Commons Attribution 4.0 (CC-BY).
ROGRESS IN APPLIED MATHEMATICS Editorial Office
Address: 1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.
Telephone: 1-514-558 6138
Http://www.cscanada.net
Http://www.cscanada.org
E-mail:[email protected] [email protected] [email protected]
Copyright © 2010 Canadian Research & Development Center of Sciences and Cultures