Title

EXACT SOLUTIONS FOR A FORCED GENERALIZATION
OF THE (2+1)-GARDNER EQUATIONS

Authors

Cesar A. Gómez S.
Departamento de Matemáticas
Universidad Nacional de Colombia
Kra. 30 No. 45-03, Bogotá, COLOMBIA

Abstract

We use an improved tanh-coth method to obtain traveling wave solutions for a new model which can be considered as a generalization of the classical (2+1)-Gardner equations with forcing term. The new model considered here, have relevance in the sense that it include the (2+1)-Gardner equation as well as the modified KdV equation and the KdV equation with forcing term. We show that from the solutions obtained for this new model, we can derived solution for classical and well know models of applied physics.

History

Received: December 22, 2016
Revised: January 29, 2017
Published: April 1, 2017

AMS Classification, Key Words

AMS Subject Classification: 35C05.
Key Words and Phrases: Improved tanh-coth method; (2+1)-Gardner equation; modified KdV equation (mKdV); KdV equation; periodic and soliton solutions; Forcing term.

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Bibliography

1

C. A. Gomez S, A. Salas S, The Cole-Hopf transformation and improved tanh-coth method applied to new integrable system (KdV6), Appl. Mathematics and Computation, 204 (2008), 957-962, doi: https://doi.org/10.1016/j.amc.2008.08.006.

2

Lin Lin, Shiyong Zhu, Yinkang Xu, Yubing Shi, Exact solutions of Gardner equations through tanh-coth method, Applied. Mathematics, 7 (2016), 2374-2381, doi: https://doi.org/10.4236/am.2016.718186.

3

C. A. Gomez S, Motlatsi Molati, Motlatsi Ramollo, Exact solutions of a generalized KdV-mKdV equation, I.J.of Nonlinear Science, 12, 3 (2011), 1-5.

4

C. A. Gomez S and A. Salas, Special symmetries to standard Riccati equations and applications, Appl. Math. and Comp., 216 (10) (2010), 3089-3096, doi: https://doi.org/10.1016/j.amc.2010.04.039.

How to Cite?

DOI: 10.12732/ijpam.v113i5.11 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 5
Pages: 643 - 648

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This work is licensed under the Creative Commons Attribution International License (CC BY).

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