Journal Menu
- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 340824, 25 pages
doi:10.1155/2012/340824
Research Article
Solving Nonlinear Partial Differential Equations by the sn-ns Method
FIZMAKO Research Group and Department of Mathematics, University of Caldas/National University of Colombia, Campus la Nubia, Manizales, Colombia
Received 2 January 2012; Accepted 30 January 2012
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 Alvaro H. Salas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- E. Fan and Y. C. Hon, “Generalized tanh method extended to special types of nonlinear equations,” Zeitschrift fur Naturforschung, vol. 57, no. 8, pp. 692–700, 2002. View at Scopus
- A.-M. Wazwaz, “The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 1002–1014, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J.-H. He and L.-N. Zhang, “Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method,” Physics Letters A, vol. 372, no. 7, pp. 1044–1047, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- R. Conte and M. Musette, “Link between solitary waves and projective Riccati equations,” Journal of Physics A, vol. 25, no. 21, pp. 5609–5623, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- W.-X. Ma and M. Chen, “Direct search for exact solutions to the nonlinear Schrödinger equation,” Applied Mathematics and Computation, vol. 215, no. 8, pp. 2835–2842, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. A. Gómez, A. H. Salas, and B. Acevedo Frias, “Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method,” Mathematical Problems in Engineering, Article ID 797084, 10 pages, 2010. View at Zentralblatt MATH
- A. Scott, Neuroscience-A Mathematical Primer, Springer-Verlag, New York, NY, USA, 2002.
- L. V. Yakushevich, Nonlinear Physics of DNA, Wiley, NewYork, NY, USA, 1998.
- W. X. Ma, H. Wu, and J. He, “Partial differential equations possessing Frobenius integrable decompositions,” Physics Letters A, vol. 364, no. 1, pp. 29–32, 2007. View at Publisher · View at Google Scholar · View at Scopus
- W. Ma, “Comment on the dimensional Kadomtsev-Petviashvili equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2663–2666, 2011. View at Publisher · View at Google Scholar
- W. X. Ma and J. H. Lee, “A transformed rational function method and exact solutions to the 3 + 1 dimensional Jimbo-Miwa equation,” Chaos, Solitons and Fractals, vol. 42, no. 3, pp. 1356–1363, 2009. View at Publisher · View at Google Scholar · View at Scopus
- W. X. Ma, T. Huang, and Y. Zhang, “A multiple exp-function method for nonlinear differential equations and its application,” Physica Scripta, vol. 82, no. 6, Article ID 065003, 2010. View at Publisher · View at Google Scholar
- W. X. Ma, X. Gu, and L. Gao, “A note on exact solutions to linear differential equations by the matrix exponential,” Advances in Applied Mathematics and Mechanics, vol. 1, no. 4, pp. 573–580, 2009. View at Publisher · View at Google Scholar
- W. X. Ma and E. Fan, “Linear superposition principle applying to Hirota bilinear equations,” Computers and Mathematics with Applications, vol. 61, no. 4, pp. 950–959, 2011. View at Publisher · View at Google Scholar
- A. Salas, “Some solutions for a type of generalized Sawada-Kotera equation,” Applied Mathematics and Computation, vol. 196, no. 2, pp. 812–817, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. H. Salas, O. G. Hurtado, and J. E. Castillo, “Computing multi-soliton solutions to Caudrey-Dodd- Gibbon equation by hirota's method,” International Journal of Physical Sciences, vol. 6, no. 34, pp. 7729–7737, 2011. View at Publisher · View at Google Scholar
- A. H. Salas, C. A. Gómez S, and B. Acevedo Frias, “Computing exact solutions to a generalized Lax-Sawada-Kotera-Ito seventh-order KdV equation,” Mathematical Problems in Engineering, Article ID 524567, 7 pages, 2010. View at Zentralblatt MATH
- A. H. Salas and C. A. Gómez S, “Exact solutions for a third-order KdV equation with variable coefficients and forcing term,” Mathematical Problems in Engineering, Article ID 737928, 13 pages, 2009. View at Zentralblatt MATH
- A. H. Salas and C. A. Gómez S., “Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation,” Mathematical Problems in Engineering, Article ID 194329, 14 pages, 2010. View at Zentralblatt MATH
- C. A. Gómez and A. H. Salas, “Exact solutions for the generalized BBM equation with variable coefficients,” Mathematical Problems in Engineering, vol. 2010, Article ID 498249, 10 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. Salas, C. A. Gómez, and J. Gonzalo Escobar Lugo, “Exact solutions for the general fifth order KdV equation by the extended tanh method,” Journal of Mathematical Sciences, vol. 1, no. 2, pp. 305–310, 2008. View at Zentralblatt MATH
- C. A. Gómez and A. H. Salas, “Exact solutions for a new integrable system (KdV6),” Journal of Mathematical Sciences, vol. 1, no. 2, pp. 401–413, 2008. View at Zentralblatt MATH
- A. Salas and C. Gómez, “A practical approach to solve coupled systems of nonlinear PDE's,” Journal of Mathematical Sciences, vol. 3, no. 1, pp. 101–107, 2009. View at Zentralblatt MATH
- C. A. Gomez and A. Salas, “Solutions for a class of fifth-order nonlinear partial differential system,” Journal of Mathematical Sciences, vol. 3, no. 1, pp. 121–128, 2009. View at Zentralblatt MATH
- A. H. Salas, “Symbolic computation of solutions for a forced Burgers equation,” Applied Mathematics and Computation, vol. 216, no. 1, pp. 18–26, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. H. Salas, “Exact solutions for the general fifth KdV equation by the exp function method,” Applied Mathematics and Computation, vol. 205, no. 1, pp. 291–297, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. A. Gómez and A. H. Salas, “The Cole-Hopf transformation and improved tanh-coth method applied to new integrable system (KdV6),” Applied Mathematics and Computation, vol. 204, no. 2, pp. 957–962, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. H. Salas, C. A. Gomez S., and J. E. Castillo Hernańdez, “New abundant solutions for the Burgers equation,” Computers & Mathematics with Applications, vol. 58, no. 3, pp. 514–520, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. A. Gómez and A. H. Salas, “The generalized tanh-coth method to special types of the fifth-order KdV equation,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 873–880, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. H. Salas, “New solutions to Korteweg-de Vries (KdV) equation by the Riccati equation expansion method,” International Journal of Applied Mathematics, vol. 22, no. 7, pp. 1169–1177, 2009. View at Zentralblatt MATH
- C. A. Gómez, “Special forms of the fifth-order KdV equation with new periodic and soliton solutions,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1066–1077, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. A. Gómez and A. H. Salas, “Exact solutions for a reaction-diffusion equation by using the generalized tanh method,” Scientia et Technica, Universidad Tecnológica de Pereira, Risaralda-Colombia, vol. 13, no. 035, pp. 409–410, 2007.
- C. A. Gómez and A. H. Salas, “The variational iteration method combined with improved generalized tanh-coth method applied to Sawada-Kotera equation,” Applied Mathematics and Computation, vol. 217, no. 4, pp. 1408–1414, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. A. Gómez and A. Salas, “Special symmetries to standard Riccati equations and applications,” Applied Mathematics and Computation, vol. 216, no. 10, pp. 3089–3096, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. A. Gómez, A. H. Salas, and B. Acevedo Frias, “New periodic and soliton solutions for the Generalized BBM and Burgers-BBM equations,” Applied Mathematics and Computation, vol. 217, no. 4, pp. 1430–1434, 2010. View at Publisher · View at Google Scholar
- A. H. Salas, J. E. Castillo, and J. G. Escobar, “About the seventh-order Kaup-Kupershmidt equation and its solutions,” Tech. Rep. 0809.2865, 2008.
- A. H. Salas, C. A. Gómez, and J. E. Castillo H., “New solutions for the modified generalized Degasperis-Procesi equation,” Applied Mathematics and Computation, vol. 215, no. 7, pp. 2608–2615, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. H. Salas, “Some exact solutions for the Caudrey-Dodd-Gibbon equation,” Tech. Rep. 0805.2969v2, 2008.
- A. H. Salas and C. A. Gómez, “El software Mathematica en la búsqueda de soluciones exactas de ecuaciones diferenciales no lineales en derivadas parciales mediante el uso de la ecuación de Riccati,” in Memorias del Primer Seminario Internacional de Tecnologias en Educación Matemática, vol. 1, pp. 379–387, Universidad Pedagógica Nacional, Santafé de Bogotá, Bogotá, Colombia, 2005.
- A. H. Salas, C. A. Gómez, and L. L. Palomá, “Travelling wave solutions to the reduced Ostrovsky equation,” International Journal of Applied Mathematics, vol. 23, pp. 249–256, 2010. View at Publisher · View at Google Scholar
- A. H. Salas, “Symbolic Computation of exact solutions to KdV equation,” Canadian Applied Mathematics Quarterly, vol. 16, no. 4, 2008.
- A. H. Salas, C. A. Gómez, and J. E. Castillo, “Symbolic computation of solutions for the general fifth-order KdV equation,” International Journal of Nonlinear Science, vol. 9, no. 4, pp. 394–401, 2010.
- C. A. Gómez and A. H. Salas, “A generalized Riccati method to solve NLPDEs,” Far East Journal of Applied Mathematics, vol. 40, no. 2, pp. 89–175, 2010.
- J. E. Castillo, A. H. Salas, and J. G. Escobar, “Exact solutions for a nonlinear model,” Applied Mathematics and Computation, vol. 217, pp. 1646–1651, 2010.
- A. H. Salas, “Exact solutions of coupled sineGordon equations,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 3930–3935, 2010. View at Publisher · View at Google Scholar · View at Scopus
- A. H. Salas, “Computing solutions to a forced KdV equation,” Nonlinear Analysis: Real World Applications, vol. 12, no. 2, pp. 1314–1320, 2011. View at Publisher · View at Google Scholar · View at Scopus
- A. H. Salas and C. A. Gómez, “Computing exact solutions for some fifth KdV equations with forcing term,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 257–260, 2008. View at Publisher · View at Google Scholar · View at Scopus
- A. H. Salas, “Exact solutions to mKdV equation with variable coefficients,” Applied Mathematics and Computation, vol. 216, no. 10, pp. 2792–2798, 2010. View at Publisher · View at Google Scholar · View at Scopus
- A. H. Salas, “Computing exact solutions to a generalized Lax seventh-order forced KdV equation (KdV7),” Applied Mathematics and Computation, vol. 216, no. 8, pp. 2333–2338, 2010. View at Publisher · View at Google Scholar · View at Scopus
- A. H. Salas and J. E. H. Castillo, “New exact solutions to sinh-cosh-Gordon equation by using techniques based on projective Riccati equations,” Computers and Mathematics with Applications, vol. 61, no. 2, pp. 470–481, 2011. View at Publisher · View at Google Scholar
- A. H. Salas and C. A. Gómez, “A note on the G0/G method and the improved tanh-coth method,” Far East Journal of Applied Mathematics, vol. 48, no. 1, pp. 1–73, 2010.
- A. H. Salas and C. A. Gómez, “Exact Solutions for the KdV6 and mKdV6 equations via tanh, coth and sech methods,” Applications and Applied Mathematics, vol. 5, no. 10, pp. 1504–1510, 2010.