- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 575679, 11 pages
Generalized Jacobi Elliptic Function Solution to a Class of Nonlinear Schrödinger-Type Equations
1Department of Mathematics, Faculty of Science, Qassim University, Buraida 51452, Saudi Arabia
2Department of Mathematics, New Valley Faculty of Education, Assiut University, El-Kharga, New Valley 71516, Egypt
Received 17 December 2010; Accepted 10 February 2011
Academic Editor: Cristian Toma
Copyright © 2011 Zeid I. A. Al-Muhiameed and Emad A.-B. Abdel-Salam. 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.
- E. Fan and Y. C. Hon, “Generalized tanh method extended to special types of nonlinear equations,” Zeitschrift fur Naturforschung A, vol. 57, no. 8, pp. 692–700, 2002.
- A. H. Bokhari, G. Mohammad, M. T. Mustafa, and F. D. Zaman, “Adomian decomposition method for a nonlinear heat equation with temperature dependent thermal properties,” Mathematical Problems in Engineering, vol. 2009, Article ID 926086, 12 pages, 2009.
- A. Wazwaz, “The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations,” Applied Mathematics and Computation, vol. 167, no. 2, pp. 1196–1210, 2005.
- J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 30, no. 3, pp. 700–708, 2006.
- M. F. El-Sabbagh and A. T. Ali, “New exact solutions for (3+1)-dimensional Kadomtsev-Petviashvili equation and generalized (2+1)-dimensional Boussinesq equation,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, no. 2, pp. 151–162, 2005.
- C. Dai and J. Zhang, “Jacobian elliptic function method for nonlinear differential-difference equations,” Chaos, Solitons and Fractals, vol. 27, no. 4, pp. 1042–1047, 2006.
- M. F. El-Sabbagh, M. M. Hassan, and E. A.-B. Abdel-Salam, “Quasi-periodic waves and their interactions in the (2 + 1)-dimensional modified dispersive water-wave system,” Physica Scripta, vol. 80, pp. 15006–15014, 2009.
- E. Fan, “Extended tanh-function method and its applications to nonlinear equations,” Physics Letters. A, vol. 277, no. 4-5, pp. 212–218, 2000.
- I. A. Hassanien, R. A. Zait, and E. A.-B. Abdel-Salam, “Multicnoidal and multitravelling wave solutions for some nonlinear equations of mathematical physics,” Physica Scripta, vol. 67, no. 6, pp. 457–463, 2003.
- Y. Ren and H. Zhang, “New generalized hyperbolic functions and auto-Bäcklund transformation to find new exact solutions of the (2+1)-dimensional NNV equation,” Physics Letters. A, vol. 357, no. 6, pp. 438–448, 2006.
- E. A. B. Abdel-Salam, “Periodic structures based on the symmetrical lucas function of the (2+1)-dimensional dispersive long-wave system,” Zeitschrift fur Naturforschung A, vol. 63, no. 10-11, pp. 671–678, 2008.
- E. A.-B. Abdel-Salam, “Quasi-periodic structures based on symmetrical Lucas function of (2+1)-dimensional modified dispersive water-wave system,” Communications in Theoretical Physics, vol. 52, no. 6, pp. 1004–1012, 2009.
- E. A.-B. Abdel-Salam, “Quasi-periodic, periodic waves, and soliton solutions for the combined KdV-mKdV equation,” Zeitschrift fur Naturforschung A, vol. 64, no. 9-10, pp. 639–645, 2009.
- E. A. B. Abdel-Salam and D. Kaya, “Application of new triangular functions to nonlinear partial differential equations,” Zeitschrift fur Naturforschung A, vol. 64, no. 1, pp. 1–7, 2009.
- E. A.-B. Abdel-Salam and Z. I. A. Al-Muhiameed, “Generalized Jacobi elliptic function method and non-travelling wave solutions,” Nonlinear Science Letters A, vol. 1, no. 4, pp. 363–372, 2010.
- H. F. Baker, Abelian Functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK, 1897.
- P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, Springer, Berlin, Germany, 1954.
- E. T. Whittaker and G. N. Watson, A Course of Modern Analysis. An Introduction to the General Theory of Infinite Processes and of Analytic Functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK, 1996.
- A. Borhanifar, M. M. Kabir, and L. Maryam Vahdat, “New periodic and soliton wave solutions for the generalized Zakharov system and (2+1)-dimensional Nizhnik-Novikov-Veselov system,” Chaos, Solitons and Fractals, vol. 42, no. 3, pp. 1646–1654, 2009.
- J. L. Zhang and M. L. Wang, “Exact solutions to a class of nonlinear Schrödinger-type equations,” Pramana Journal of Physics, vol. 67, no. 6, pp. 1011–1022, 2006.
- M. Florjańczyk and L. Gagnon, “Exact solutions for a higher-order nonlinear Schrödinger equation,” Physical Review A, vol. 41, no. 8, pp. 4478–4485, 1990.
- D.-J. Huang, D.-S. Li, and H.-Q. Zhang, “Explicit and exact travelling wave solutions for the generalized derivative Schrödinger equation,” Chaos, Solitons and Fractals, vol. 31, no. 3, pp. 586–593, 2007.
- S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion-managed optical fibers,” Optics Letters, vol. 22, no. 6, pp. 372–374, 1997.
- H. W. Schürmann, “Traveling-wave solutions of the cubic-quintic nonlinear Schrödinger equation,” Physical Review E, vol. 54, no. 4, pp. 4312–4320, 1996.