- 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 2013 (2013), Article ID 594975, 10 pages
Conservation Laws of Two -Dimensional Nonlinear Evolution Equations with Higher-Order Mixed Derivatives
Department of Mathematics, Dezhou University, Dezhou 253023, China
Received 12 May 2013; Accepted 29 June 2013
Academic Editor: Chaudry Masood Khalique
Copyright © 2013 Li-hua Zhang. 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.
- T. B. Benjamin, “The stability of solitary waves,” Proceedings of the Royal Society A, vol. 328, no. 1573, pp. 153–183, 1972.
- R. J. Knops and C. A. Stuart, “Quasi convexity and uniqueness of equilibrium solutions in nonlinear elasticity,” in The Breadth and Depth of Continuum Mechanics, pp. 473–489, Springer, Berlin, Germany, 1986.
- P. D. Lax, “Integrals of nonlinear equations of evolution and solitary waves,” Communications on Pure and Applied Mathematics, vol. 21, no. 5, pp. 467–490, 1968.
- E. Noether, “Invariante variations problem,” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, vol. 2, pp. 235–257, 1918.
- N. H. Ibragimov, “A new conservation theorem,” Journal of Mathematical Analysis and Applications, vol. 333, no. 1, pp. 311–328, 2007.
- N. H. Ibragimov, “Quasi-self-adjoint differential equations,” Archives of ALGA, vol. 4, pp. 55–60, 2007.
- N. H. Ibragimov, “Integrating factors, adjoint equations and lagrangians,” Journal of Mathematical Analysis and Applications, vol. 318, no. 2, pp. 742–757, 2006.
- N. H. Ibragimov, M. Torrisi, and R. Tracinà, “Quasi self-adjoint nonlinear wave equations,” Journal of Physics A, vol. 43, no. 44, p. 442001, 2010.
- L.-H. Zhang, “Conservation laws of the -dimensional KP equation and Burgers equation with variable coefficients and cross terms,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4865–4879, 2013.
- L.-H. Zhang, “Self-adjointness and conservation laws of two variable coefficient nonlinear equations of Schrödinger type,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 3, pp. 453–463, 2013.
- M. S. Bruzón, M. L. Gandarias, and N. H. Ibragimov, “Self-adjoint sub-classes of generalized thin film equations,” Journal of Mathematical Analysis and Applications, vol. 357, no. 1, pp. 307–313, 2009.
- M. L. Gandarias, M. Redondo, and M. S. Bruzón, “Some weak self-adjoint Hamilton-Jacobi-Bellman equations arising in financial mathematics,” Nonlinear Analysis: Real World Applications, vol. 13, no. 1, pp. 340–347, 2012.
- R. Naz, F. M. Mahomed, and D. P. Mason, “Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics,” Applied Mathematics and Computation, vol. 205, no. 1, pp. 212–230, 2008.
- B. Xu and X.-Q. Liu, “Classification, reduction, group invariant solutions and conservation laws of the Gardner-KP equation,” Applied Mathematics and Computation, vol. 215, no. 3, pp. 1244–1250, 2009.
- E. Yaşar, “On the conservation laws and invariant solutions of the mKdV equation,” Journal of Mathematical Analysis and Applications, vol. 363, no. 1, pp. 174–181, 2010.
- R. Narain and A. H. Kara, “Conservation laws of high-order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives,” Journal of Physics A, vol. 43, no. 8, p. 085205, 2010.
- Y. Yu, Q. Wang, and H. Zhang, “The extension of the Jacobi elliptic function rational expansion method,” Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 5, pp. 702–713, 2007.
- C. Dai, F. Liu, and J. Zhang, “Novel types of interactions between solitons in the -dimensional asymmetric Nizhnik-Novikov-Veselov system,” Chaos, Solitons & Fractals, vol. 36, no. 2, pp. 437–445, 2008.
- L.-H. Zhang, X.-Q. Liu, and C.-L. Bai, “Symmetry, reductions and new exact solutions of ANNV equation through Lax pair,” Communications in Theoretical Physics, vol. 50, no. 1, pp. 1–6, 2008.
- L. Wang, Z.-Z. Dong, and X.-Q. Liu, “Symmetry reductions, exact solutions and conservation laws of asymmetric Nizhnik-Novikov-Veselov equation,” Communications in Theoretical Physics, vol. 49, no. 1, pp. 1–8, 2008.
- A.-M. Wazwaz, “Exact solutions of compact and noncompact structures for the KP-BBM equation,” Applied Mathematics and Computation, vol. 169, no. 1, pp. 700–712, 2005.
- A.-M. Wazwaz, “The extended tanh method for new compact and noncompact solutions for the KP-BBM and the ZK-BBM equations,” Chaos, Solitons and Fractals, vol. 38, no. 5, pp. 1505–1516, 2008.
- M. A. Abdou, “Exact periodic wave solutions to some nonlinear evolution equations,” International Journal of Nonlinear Science, vol. 6, no. 2, pp. 145–153, 2008.
- K. R. Adem and C. M. Khalique, “Exact solutions and conservation laws of a -dimensional nonlinear KP-BBM equation,” Abstract and Applied Analysis, vol. 2013, Article ID 791863, 5 pages, 2013.