Cross-kink multi-soliton solutions for the (3+1)-D Jimbo-Miwa equation

Abstract

In this paper, by using bilinear form and extended three-wave type of ans¨atz approach, we obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breather-type of kink three-soliton solutions, the cross-kink four-soliton solutions, the doubly periodic breathertype of soliton solutions and the doubly periodic breather-type of cross-kink two-soliton solutions. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

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Xu, Z. and Chen, H. (2012) Cross-kink multi-soliton solutions for the (3+1)-D Jimbo-Miwa equation. Open Journal of Applied Sciences, 2, 215-218. doi: 10.4236/ojapps.2012.24B049.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] W.X.Ma, E.G.Fan, Linear superposition principle applying to Hirota bilinear equations, Computers and Mathematics with Applications. 61 (2011) 950-959.
[2] X.Q.Liu, H.L.Chen, Y.Q.Lv, Explicit solutions of the generalized KdV equation with higher order nonlinearity, Appl. Math. Comput. 171(2005)315-319.
[3] Z.D.Dai, J. Huang, M.R.Jiang, S.H.Wang, Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint, Chaos Soliton and Fractals. 26 (2005) 1189-1194.
[4] M. Jimbo, T. Miwa, Publ. Res. Inst. Math. Sci. 19 (1983) 943; MathSciNet.
[5] Z.D.Dai, Z.T.Li, Z.J.Liu, D.L.Li, Exact cross kink-wave solutions and resonance for the JimboCMiwa equation, Physica A 384 (2007) 285C290.
[6] Z.T.Li, Z.D.Dai, J.Liu, Exact three-wave solutions for the (3 + 1)-dimensional Jimbo-Miwa equation, Computers and Mathematics with Applications 61 (2011) 2062C2066.
[7] Z.H.Xu, D.Q.Xian, New periodic solitary-wave solutions for the Benjiamin Ono equation, Applied Mathematics and Computation. 215 (2010) 4439-4442.
[8] K.W.Chow, A class of doubly periodic waves for nonlinear evolution equations, Wave Motion. 35 (2002) 71-90.
[9] Z.H.Xu, X.Q. Liu, Explicit Peaked Wave Solution to the Generalized Camassa-Holm Equation, Acta Mathematicae Applicatae Sinica. 26(2)(2010)277-282.

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