- 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 198398, 11 pages
Travelling Wave Solutions of the Schrödinger-Boussinesq System
1Department of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
2Young Researchers Club, Ardabil Branch, Islamic Azad University, P.O. Box. 5616954184, Ardabil, Iran
Received 16 August 2012; Accepted 4 October 2012
Academic Editor: Mohammad Mursaleen
Copyright © 2012 Adem Kılıcman and Reza Abazari. 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.
- C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, vol. 139 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1999.
- T. Kato, “On nonlinear Schrödinger equations,” Annales de l'Institut Henri Poincaré. Physique Théorique, vol. 46, no. 1, pp. 113–129, 1987.
- J. Boussinesq, “Théorie des ondes et des remous qui se propagent le long dun canal rectangulaire horizontal, en communiquant au liquide continu dans 21 ce canal des vitesses sensiblement pareilles de la surface au fond,” Journal de Mathématiques Pures et Appliquées, vol. 17, no. 2, pp. 55–108, 1872.
- O. V. Kaptsov, “Construction of exact solutions of the Boussinesq equation,” Journal of Applied Mechanics and Technical Physics, vol. 39, pp. 389–392, 1998.
- V. Zakharov, “On stochastization of one-dimensional chains of nonlinear oscillators,” Journal of Experimental and Theoretical Physics, vol. 38, pp. 110–108.
- F. Falk, E. Laedke, and K. Spatschek, “Stability of solitary-wave pulses in shape-memory alloys,” Physical Review B, vol. 36, no. 6, pp. 3031–3041, 1978.
- V. Makhankov, “On stationary solutions of Schrödinger equation with a self-consistent potential satisfying Boussinesqs equations,” Physics Letters A, vol. 50, pp. 42–44, 1974.
- N. Yajima and J. Satsuma, “Soliton solutions in a diatomic lattice system,” Progress of Theoretical Physics, vol. 62, no. 2, pp. 370–378, 1979.
- M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, vol. 4, SIAM, Philadelphia, Pa, USA, 1981.
- M. R. Miurs, Bäcklund Transformation, Springer, Berlin, Germany, 1978.
- R. Hirota, “Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons,” Physical Review Letters, vol. 27, pp. 1192–1194, 1971.
- J. Weiss, M. Tabor, and G. Carnevale, “The Painlevé property for partial differential equations,” Journal of Mathematical Physics, vol. 24, no. 3, pp. 522–526, 1983.
- N. C. Freeman and J. J. C. Nimmo, “Soliton solutions of the Korteweg-de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique,” Proceedings of the Royal Society of London Series A, vol. 389, no. 1797, pp. 319–329, 1983.
- W. Malfliet and W. Hereman, “The tanh method—I. Exact solutions of nonlinear evolution and wave equations,” Physica Scripta, vol. 54, no. 6, pp. 563–568, 1996.
- F. Xu, “Application of Exp-function method to symmetric regularized long wave (SRLW) equation,” Physics Letters A, vol. 372, no. 3, pp. 252–257, 2008.
- F. Tascan, A. Bekir, and M. Koparan, “Travelling wave solutions of nonlinear evolution equations by using the first integral method,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 1810–1815, 2009.
- M. Wang, X. Li, and J. Zhang, “The ()-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Physics Letters A, vol. 372, no. 4, pp. 417–423, 2008.
- R. Abazari, “The ()-expansion method for Tzitzéica type nonlinear evolution equations,” Mathematical and Computer Modelling, vol. 52, no. 9-10, pp. 1834–1845, 2010.
- R. Abazari, “The ( )-expansion method for the coupled Boussinesq equations,” Procedia Engineering, vol. 10, pp. 2845–2850, 2011.