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The Lump Solutions of the (1 + 1)-Dimensional Ito-Equation

DOI: 10.4236/ojapps.2019.93011, PP. 121-125

Keywords: Ito-Equation, Lump Solution, Solitons, Hirota’s Bilinear Method

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Abstract:

In this paper, several kinds of lump solutions for the (1 + 1)-dimensional Ito-equation are introduced. The proposed method in this work is based on a Hirota bilinear differential equation. The form of the solutions to the equation is constructed and the solutions are improved through analysis and symbolic computations with Maple. Finally, figure of the solution is made for specific examples for the lump solutions.

References

[1]  Miura, R.M. (1978) Backlund Transformation. Springer-Verlag, Berlin.
[2]  Rogers, C. and Shadwick, W.F. (1982) Backlund Transformations and Their Applications.
[3]  Matveev, V.B. and Salle, M.A. (1991) Darboux Transformation and Solitons. Journal of Neurochemistry, 42, 1667-1676.
[4]  Hirota, R. (2004) The Direct Method in Soliton Theory. Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511543043
[5]  Ma, W.X. (2015) Lump Solutions to the Kadomtsev-Petviashvili Equation. Physics Letters A, 379, 1975-1978.
[6]  Tan, W. and Dai, Z. (2017) Spatiotemporal Dynamics of Lump Solution to the (1 + 1)-Dimensional Benjamin-Ono Equation. Nonlinear Dynamics, 89, 2723–2728.
https://doi.org/10.1007/s11071-017-3620-0
[7]  Yu, J.P. and Sun, Y.L. (2016) Study of Lump Solutions to Dimensionally Reduced Generalized KP Equations. Nonlinear Dynamics, 87, 1-9.
[8]  Yang, J.Y., Ma, W.X. and Qin, Z. (2017) Lump and Lump-Soliton Solutions to the (2 + 1)-Dimensional Ito Equation. Analysis. Mathematical Physics, No. 1, 1-10.
[9]  Zaharov, V.E. (1976) Exact Solutions in the Problem of Parametric Interaction of Three-Dimensional Wave Packets. Doklady Akademii Nauk Sssr, 228, 1314-1316.
[10]  Craik, A.D.D. (1978) Evolution in Space and Time of Resonant Wave Triads. II. A Class of Exact Solutions. Proceedings of the Royal Society A, 363, 257-269.
https://doi.org/10.1098/rspa.1978.0167
[11]  Ma, W.X. and You, Y. (2005) Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions. Transactions of the American Mathematical Society, 357, 1753-1778.
https://doi.org/10.1090/S0002-9947-04-03726-2
[12]  Weiss, J., Tabor, M. and Carnevale, G. (1983) The Painleve Property for Partial Differential Equations. Journal of Mathematical Physics, 24, 522-526.
https://doi.org/10.1063/1.525721
[13]  Liu, H., Li, J. and Liu, L. (2013) The Recursion Operator Method for Generalized Symmetries and Bäcklund Transformations of the Burgers’ Equations. Journal of Applied Mathematics and Computing, 42, 159-170.
https://doi.org/10.1007/s12190-012-0633-1

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