- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- 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
Advances in Mathematical Physics
Volume 2013 (2013), Article ID 282390, 5 pages
Recursion Operator and Local and Nonlocal Symmetries of a New Modified KdV Equation
Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China
Received 3 September 2013; Accepted 4 November 2013
Academic Editor: Wen-Xiu Ma
Copyright © 2013 Qian Suping and Li Xin. 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.
- W. I. Fushchich and W. M. Shtelen, “On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter,” Journal of Physics A, vol. 22, no. 18, pp. L887–L890, 1989.
- J. Dodd, “Spectral stability of undercompressive shock profile solutions of a modified KdV-Burgers equation,” Electronic Journal of Differential Equations, vol. 2007, pp. 135–13, 2007.
- W. Malfliet and W. Hereman, “The tanh method: II. Perturbation technique for conservative systems,” Physica Scripta, vol. 54, no. 6, pp. 569–575, 1996.
- T. R. Marchant and N. F. Smyth, “Pulse evolution for Marangoni-Bénard convection,” Mathematical and Computer Modelling, vol. 28, no. 10, pp. 45–58, 1998.
- M. A. Allen and G. Rowlands, “A solitary-wave solution to a perturbed KdV equation,” Journal of Plasma Physics, vol. 64, no. 4, pp. 475–480, 2000.
- J. R. Yan, L. X. Pan, and G. H. Zhou, “Soliton perturbations of the modified Korteweg de Vries equation,” Communications in Theoretical Physics, vol. 34, no. 3, pp. 463–470, 2000.
- S. Y. Lou, “Consistent riccati expansion and solvability,” http://arxiv.org/abs/1308.5891v2.
- X. Jiao, R. Yao, and S. Y. Lou, “Approximate similarity reduction for singularly perturbed Boussinesq equation via symmetry perturbation and direct method,” Journal of Mathematical Physics, vol. 49, no. 9, Article ID 093505, 11 pages, 2008.
- C. H. Gu, B. Guo, Y. Li et al., Soliton Theory and Its Applications, Zhejiang Hangzhou, 1990.
- P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107, Springer, New York, NY, USA, 1993.
- S.-P. Qian and L.-X. Tian, “Modification of the Clarkson-Kruskal direct method for a coupled system,” Chinese Physics Letters, vol. 24, no. 10, pp. 2720–2723, 2007.
- X. R. Hu, S. Y. Lou, and Y. Chen, “Explicit solutions from eigenfunction symmetry of the korteweg—de vries equation,” Physical Review E, vol. 85, no. 5, Article ID 056607, 8 pages, 2012.
- S. Y. Lou, X. Hu, and Y. Chen, “Nonlocal symmetries related to Bäcklund transformation and their applications,” Journal of Physics A, vol. 45, no. 15, Article ID 155209, 14 pages, 2012.