By the complete
discrimination system for polynomial method, we obtained the classification of
single traveling wave solutions to the generalized strong nonlinear Boussinesq
equation without dissipation terms in p=1.
References
[1]
Fan, E.G. (1998) A Note on the Homogenous Balance Method. Physics Letters A, 246, 403-406. http://dx.doi.org/10.1016/S0375-9601(98)00547-7
[2]
Ablowitz, M.J. and Clarkson, P.A. (1991) Solitons, Non-Linear Evolution Equations and Inverse Scattering Transform. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511623998
[3]
Hirota, R. (1973) Exact Envelope-Soliton of a Nonlinear Wave Equation. Journal of Mathematical Physics, 14, 805-813. http://dx.doi.org/10.1063/1.1666399
[4]
Ma, W.X. and Fuchssteiner, B. (1996) Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation. International Journal of Non-Linear Mechanics, 31, 329-338. http://dx.doi.org/10.1016/0020-7462(95)00064-X
[5]
Ma, W.X. (1993) Travelling Wave Solutions to a Seventh Order Generalized KdV Equation. Physics Letters A, 180, 221-224.
[6]
Liu, C.S. (2010) Applications of Complete Discrimination System for Polynomial for Classifications of Traveling Wave Solutions to Nonlinear Differential Equations. Computer Physics Communications, 181, 317-324. http://dx.doi.org/10.1016/j.cpc.2009.10.006
[7]
Liu, C.S. (2007) Classification of All Single Traveling Wave Solutions to Calogero-Focas Equation. Communications in Theoretical Physics (Beijing), 48, 601-604. http://dx.doi.org/10.1088/0253-6102/48/4/004
[8]
Liu, C.S. (2006) Direct integral method, complete discrimination system for polynomial and applications to classifications of all single travelling wave solutions to nonlinear differential equations: a survey. arXiv: nlin/0609058v1
[9]
Zhang, W.G. and Tao, T. (2008) Analysis of Solitary-Wave Shape and Solutions of the Generalized Strong Nonlinear Boussinesq Equation. Acta Mathematica Sientia, 28A, 086-095.
[10]
Whitham, G.B. (1974) Linear and Nonlinear Wave. Springer, New York.
[11]
Zhakarov, V.E. (1974) On Stochastization of One-Dimensional Chains of Nonlinear Oscillation. Soviet Physics-JETP, 38, 108-110.
[12]
McKean, H.P. (1981) Boussinesq’s Equation on the Circle. Pure and Applied Mathematics, 34, 599-690. http://dx.doi.org/10.1002/cpa.3160340502
[13]
Manoranjan, V.S., et al. (1985) Numerical Solution of the Good Boussinesq Equation. SIAM: SIAM Journal on Scientific Computing, 5, 946-957.
[14]
Weiss, J. (1985) The Painlevé Property and Backlund Transformation for the Sequence of Boussinesq Equations. Journal of Mathematical Physics, 26, 258-269. http://dx.doi.org/10.1063/1.526655
[15]
Hu, X.G., Wu, Y.H. and Li, L. (2013) New Traveling Wave Solutions of the Boussinesq Equation Using a New Generalized Mapping Method. Journal of Basic and Applied Physics, 2, 68-77. http://dx.doi.org/10.5963/JBAP0202005
[16]
Zakharov, V.E., et al. (1984) Theory of Solitons: The Iverse Scattering Method. Plenum Press, New York.
[17]
Hirota, R. (1973) Exact N-Soliton Solutions of the Wave Equation of Long Wave Shallow-Water and in Nonlinear Lattices. Journal of Mathematical Physics, 14, 810-814. http://dx.doi.org/10.1063/1.1666400
