Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/solutions-of-jimbo-miwa-equation-and-konopelchenko-dubrovsky-equations-gFshjJ27mt
References (27)
-
Xiaoping Xu (2007)
Flag Partial Differential Equations and Representations of Lie AlgebrasActa Applicandae Mathematicae, 102
-
Lina Song, Hong-qing Zhang (2007)
New exact solutions for the Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computationAppl. Math. Comput., 187
-
B. Dorizzi, B. Grammaticos, A. Ramani, P. Winternitz (1986)
Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable?Journal of Mathematical Physics, 27
-
J. Rubin, P. Winternitz (1990)
Point symmetries of conditionally integrable nonlinear evolution equationsJournal of Mathematical Physics, 31
-
M. Wadati, K. Konno, Y. Ichikawa (1979)
New Integrable Nonlinear Evolution EquationsJournal of the Physical Society of Japan, 47
-
Lin Ji, Lou Sen-yue, W. Kelin (2001)
Multi-soliton Solutions of the Konopelchenko-Dubrovsky EquationChinese Physics Letters, 18
-
J. Hunter, R. Saxton (1991)
Dynamics of director fieldsSiam Journal on Applied Mathematics, 51
-
Xiaoping Xu (2007)
Stable-Range Approach to the Equation of Nonstationary Transonic Gas FlowsarXiv: Fluid Dynamics
-
Lina Song, Hong-qing Zhang (2008)
Application of the extended homotopy perturbation method to a kind of nonlinear evolution equationsAppl. Math. Comput., 197
-
Zhang Sheng (2006)
The periodic wave solutions for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equationsChaos Solitons & Fractals, 30
-
Xiaoping Xu (2008)
Stable-Range Approach to Short Wave and Khokhlov-Zabolotskaya EquationsActa Applicandae Mathematicae, 106
-
E. Fan (2003)
An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equationsJ. Phys. A, 36
-
A. Maccari (1999)
A new integrable Davey–Stewartson-type equationJournal of Mathematical Physics, 40
-
M. Abdou (2008)
Generalized solitonary and periodic solutions for nonlinear partial differential equations by the Exp-function methodNonlinear Dynamics, 52
-
M. Jimbo, T. Miwa (1983)
Solitons and infinite dimensional Lie algebrasPubl. RIMS Kyoto Univ., 19
-
S. Lou, J. Weng (1995)
Generalized W ∞ symmetry algebra of the conditionally integrable nonlinear evolution equationJ. Math. Phys., 36
-
M. Jimbo, T. Miwa (1983)
Solitons and Infinite Dimensional Lie AlgebrasPublications of The Research Institute for Mathematical Sciences, 19
-
Deng‐Shan Wang, Hong-qing Zhang (2005)
Further improved F-expansion method and new exact solutions of Konopelchenko–Dubrovsky equationChaos Solitons & Fractals, 25
-
W. Hong, Kwang-Sik Oh (2000)
New solitonic solutions to a (3+1)-dimensional Jimbo-Miwa equationComputers & Mathematics With Applications, 39
-
B. Konopelchenko, V. Dubrovsky (1984)
Some new integrable nonlinear evolution equations in 2 + 1 dimensionsPhysics Letters A, 102
-
A. Wazwaz (2007)
New kinks and solitons solutions to the (2+1) -dimensional Konopelchenko-Dubrovsky equationMath. Comput. Model., 45
-
Zhi Hongyan (2008)
Lie point symmetry and some new soliton-like solutions of the Konopelchenko-Dubrovsky equationsAppl. Math. Comput., 203
-
E. Fan (2003)
An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinea -
T. Xia, Zhuosheng Lü, Hong-qing Zhang (2004)
Symbolic computation and new families of exact soliton-like solutions of Konopelchenko–Dubrovsky equationsChaos Solitons & Fractals, 20
-
Zhang Sheng (2007)
Symbolic computation and new families of exact non-travelling wave solutions of (2 + 1)-dimensional Konopelchenko–Dubrovsky equationsChaos Solitons & Fractals, 31
-
S. Lou, Jian Weng (1995)
Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equationJournal of Mathematical Physics, 36
-
S. Zhang, T. Xia (2006)
A generalized F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equationsAppl. Math. Comput., 183
- Publisher
- Springer Journals
- Copyright
- Copyright © 2010 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-009-9559-5
- Publisher site
- See Article on Publisher Site
Abstract
The Jimbo-Miwa equation is the second equation in the well known KP hierarchy of integrable systems, which is used to describe certain interesting (3+1)-dimensional waves in physics but not pass any of the conventional integrability tests. The Konopelchenko-Dubrovsky equations arose in physics in connection with the nonlinear weaves with a weak dispersion. In this paper, we obtain two families of explicit exact solutions with multiple parameter functions for these equations by using Xu’s stable-range method and our logarithmic generalization of the stable-range method. These parameter functions make our solutions more applicable to related practical models and boundary value problems.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Jan 13, 2010