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

Affiliation(s)

Applied Technology College, Southwest University of Science and Technology, Mianyang.

School of Science, Southwest University of Science and Technology, Mianyang 621010, China..

Applied Technology College, Southwest University of Science and Technology, Mianyang.

School of Science, Southwest University of Science and Technology, Mianyang 621010, China..

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.

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.

Cite this paper

nullXu, 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.

nullXu, Z. and Chen, H. (2012) Cross-kink multi-soliton solutions for the (3+1)-D Jimbo-Miwa equation.

References

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[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.

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[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.

[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.