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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 256019, 7 pages
Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation
Department of Mathematics, Faculty of Sciences, University of Chouaïb Doukkali, BP 20, El-Jadida, Morocco
Received 6 October 2013; Accepted 2 January 2014; Published 17 February 2014
Academic Editor: Chaudry Masood Khalique
Copyright © 2014 Abdelfattah El Achab. 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.
- M. L. Wang, “Solitary wave solutions for variant Boussinesq equations,” Physics Letters A, vol. 199, no. 3-4, pp. 169–172, 1995.
- E. J. Parkes and B. R. Duffy, “Travelling solitary wave solutions to a compound KdV-Burgers equation,” Physics Letters A, vol. 229, no. 4, pp. 217–220, 1997.
- Z. Fu, S. Liu, S. Liu, and Q. Zhao, “New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations,” Physics Letters A, vol. 290, no. 1-2, pp. 72–76, 2001.
- M. Wang and Y. Zhou, “The periodic wave solutions for the Klein-Gordon-Schrödinger equations,” Physics Letters A, vol. 318, no. 1-2, pp. 84–92, 2003.
- J.-H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 695–700, 2005.
- J.-H. He, “Homotopy perturbation method for bifurcation of nonlinear problems,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, no. 2, pp. 207–208, 2005.
- J. Li and Z. Liu, “Smooth and non-smooth traveling waves in a nonlinearly dispersive equation,” Applied Mathematical Modelling, vol. 25, no. 1, pp. 41–56, 2000.
- J. Li and Z. Liu, “Traveling wave solutions for a class of nonlinear dispersive equations,” Journal of Chinese Annals of Mathematics B, vol. 23, no. 3, pp. 397–418, 2002.
- H. W. Schürmann, “Traveling-wave solutions of the cubic-quintic nonlinear Schrödinger equation,” Physical Review E, vol. 54, no. 4, pp. 4312–4320, 1996.
- H. W. Schürmann, V. S. Serov, and J. Nickel, “Superposition in nonlinear wave and evolution equations,” International Journal of Theoretical Physics, vol. 45, no. 6, pp. 1057–1073, 2006.
- J. Nickel, V. S. Serov, and H. W. Schürmann, “Some elliptic traveling wave solutions to the Novikov-Veselov equation,” Progress in Electromagnetics Research, vol. 61, pp. 323–331, 2006.
- P. Rosenau and J. M. Hyman, “Compactons: solitons with finite wavelength,” Physical Review Letters, vol. 70, no. 5, pp. 564–567, 1993.
- Z. Liu and J. Li, “Bifurcations of solitary waves and domain wall waves for KdV-like equation with higher order nonlinearity,” International Journal of Bifurcation and Chaos, vol. 12, no. 2, pp. 397–407, 2002.
- A. M. Wazwaz, “New solitary-wave special solutions with compact support for the nonlinear dispersive equations,” Chaos, Solitons and Fractals, vol. 13, no. 2, pp. 321–330, 2002.
- L. Zhang, L.-Q. Chen, and X. Huo, “Peakons and periodic cusp wave solutions in a generalized Camassa-Holm equation,” Chaos, Solitons and Fractals, vol. 30, no. 5, pp. 1238–1249, 2006.
- Y. A. Li and P. J. Olver, “Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Compactons and peakons,” Discrete and Continuous Dynamical Systems, vol. 3, no. 3, pp. 419–432, 1997.
- Y. A. Li and P. J. Olver, “Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. II. Complex analytic behavior and convergence to non-analytic solutions,” Discrete and Continuous Dynamical Systems, vol. 4, no. 1, pp. 159–191, 1998.
- P. Rosenau, “Nonlinear dispersion and compact structures,” Physical Review Letters, vol. 73, no. 13, pp. 1737–1741, 1994.
- Z. Yan, “New families of solitons with compact support for Boussinesq-like equations with fully nonlinear dispersion,” Chaos, Solitons and Fractals, vol. 14, no. 8, pp. 1151–1158, 2002.
- Y. Zhu, “Exact special solutions with solitary patterns for Boussinesq-like equations with fully nonlinear dispersion,” Chaos, Solitons and Fractals, vol. 22, no. 1, pp. 213–220, 2004.
- Y. Zhu and C. Lu, “New solitary solutions with compact support for Boussinesq-like equations with fully nonlinear dispersion,” Chaos, Solitons & Fractals, vol. 32, no. 2, pp. 768–772, 2007.
- Z. Liu, Q. Lin, and Q. Li, “Integral approach to compacton solutions of Boussinesq-like equation with fully nonlinear dispersion,” Chaos, Solitons and Fractals, vol. 19, no. 5, pp. 1071–1081, 2004.
- A.-M. Wazwaz, “Nonlinear variants of the improved Boussinesq equation with compact and noncompact structures,” Computers & Mathematics with Applications, vol. 49, no. 4, pp. 565–574, 2005.
- S. Lai and Y. Wu, “The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation,” Discrete and Continuous Dynamical Systems B, vol. 3, no. 3, pp. 401–408, 2003.
- S. Lai, Y. H. Wu, and X. Yang, “The global solution of an initial boundary value problem for the damped Boussinesq equation,” Communications on Pure and Applied Analysis, vol. 3, no. 2, pp. 319–328, 2004.
- A.-M. Wazwaz, “Compactons and solitary wave solutions for the Boussinesq wave equation and its generalized form,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 529–535, 2006.
- K. Weierstrass, Mathematische werke V Johnson, New York, NY, USA, 1915.
- E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge, UK, 1996.
- K. Chandrasekharan, Elliptic Functions, Springer, Berlin, Germany, 1985.
- M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 9th edition, 1972.
- S. Lai, “Different physical structures of solutions for a generalized Boussinesq wave equation,” Journal of Computational and Applied Mathematics, vol. 231, no. 1, pp. 311–318, 2009.