Trial Equation Method for Solving the Improved Boussinesq Equation

Yang Li^{*}

Show more

References

[1] M. J. Ablowitz and P. A. Clarson, “Solitons, Nonlinear Evolution Equations and Inverse Scattering,” Cambridge University Press, New York, 1991. http://dx.doi.org/10.1017/CBO9780511623998

[2] R. Hirota, “Exact Envelope-Soliton Solutions of a Nonlinear Wave Equation,” Journal of Mathematical Physics, Vol. 14, No. 7, 1973, p. 805. http://dx.doi.org/10.1063/1.1666399

[3] R. Hirota and J. Satsuma, “Soliton Solutions of a Coupled Korteweg-de Vries Equation,” Physical Letters A, Vol. 85, No. 8-9, 1981, pp. 407-408. http://dx.doi.org/10.1016/0375-9601(81)90423-0

[4] E. Fan, “Extended Tank-Function Method and Its Applications to Nonlinear Equations,” Physical Letters A, Vol. 277, No. 4, 2000, pp. 212-218.

[5] C. T. Yan, “A Simple Transformation for Nonlinear Waves,” Physical Letters A, Vol. 224, No. 1-2, 1996, pp. 77-84.

http://dx.doi.org/10.1016/S0375-9601(96)00770-0

[6] M. Wang, “Solitary Wave Solutions for Variant Boussinesq Equations,” Physical Letters A, Vol. 199, No. 3, 1995, pp. 169-172.

[7] M. L. Wang, “Solitary Wave Solutions for Variant Boussinesq Equations,” Physical Letters A, Vol. 199, No. 3-4, 1995, pp. 169-172. http://dx.doi.org/10.1016/0375-9601(95)00092-H

[8] W. X. Ma and J. H. Lee, “A Transformed Rational Function Method and Exact Solutions to the 3 + 1 Dimensional Jimbo-Miwa Equation,” Chaos, Solitons and Fractals, Vol. 42, No. 3, 2009, pp. 1356-1363.

http://dx.doi.org/10.1016/j.chaos.2009.03.043

[9] “Applications,” Communications in Theoretical Physics, Vol. 45, No. 2, 2006, pp. 219-223.

[10] C. S. Liu, “Trial Equation Method and Its Applications to Nonlinear Evolution Equations,” Acta Physical Sinica, Vol. 54, 2005, p. 2505 (in Chinese).

[11] C. S. Liu, “Using Trial Equation Method to Solve the Exact Solutions for Two Kinds of KdV Equations with Variable Coefficients,” Acta Physical Sinica, Vol. 54, No. 10, 2005, p. 4506.

[12] C. S. Liu, “Representations and Classification of Traveling Wave Solutions to Sinh-Gordon Equation,” Communications in Theoretical Physics, Vol. 49, 2008, pp. 153-158. http://dx.doi.org/10.1088/0253-6102/49/1/33

[13] C. S. Liu, “Solution of ODE and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations,” Communications in Theoretical Physics, Vol. 49, 2008, pp. 291-296. http://dx.doi.org/10.1088/0253-6102/49/2/07

[14] C. S. Liu, “Applications of Complete Discrimination System for Polynomial for Classifications of Traveling Wave Solutions to Nonlinear Differential Equations,” Computer Physics Communications, Vol. 181, 2010, pp. 317-324.

http://dx.doi.org/10.1016/j.cpc.2009.10.006

[15] C. S. Liu, “Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation,” Communications in Theoretical Physics, Vol. 48, 2007, pp. 601-604. http://dx.doi.org/10.1088/0253-6102/48/4/004

[16] C. S. Liu, “All Single Traveling Wave Solutions to Nizhnok-Novikov-Veselov Equation,” Communications in Theoretical Physics, Vol. 45, 2006, pp. 991-992. http://dx.doi.org/10.1088/0253-6102/45/6/006

[17] P. L. Christiansen and V. Muto, “Physica D 68,” 1993. http://dx.doi.org/10.1016/0167-2789(93)90033-W

[18] Z. Yang and B. Y. C. Hon, “An Improved Modified Extended Tanh-Function Method,” Zeitschrift fur Naturforschung A— Journal of Physical Sciences, Vol. 61, No. 3-4, 2006, pp. 103-115.