GENERALIZED 2+1 −DIMENSIONAL BREAKING SOLITON EQUATION

Year 2011, Volume: 01 Issue: 1, 69 - 74, 01.06.2011

Abdul-majid Wazwaz

Abstract

In this work, a general 2+1 -dimensional breaking soliton equation is investigated. The Hereman’s simplified method is applied to derive multiple soliton solutions, hence to confirm the model integrability.

Keywords

Breaking soliton equation , multiple soliton solutions , multiple singular solitonsolutions

References

• Bogoyavlenskii, O.I., (1990), Breaking solitons in 2+1-dimensional integrable equations, Uspekhi Mat. Nauk., 45(4), 17-27.
• Wazwaz, A.M., (2010), Integrable (2 + 1)-dimensional and (3 + 1)-dimensional breaking soliton equations, Phys. Scr., 81, 035005.
• Ma, S.-H., Peng, J. and Zhang, C., (2009), New exact solutions of the (2+1)-dimensional breaking soliton system via an extended mapping method, Chaos, Solitons and Fractals, 46, 210-214.
• Gao, Y.-T. and Tian, B., (1995), New family of overturning soliton solutions for a typical breaking soliton equation, Comput. Math. Applic., 12, 97-100.
• Hirota, R., (1974), A new form of B¨acklund transformations and its relation to the inverse scattering problem, Progress of Theoretical Physics, 52(5), 1498-1512.
• Hirota, R., (2004), The Direct Method in Soliton Theory, Cambridge University Press, Cambridge.
• Hirota, R., (1971), Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons, Physical Review Letters, 27(18), 1192-1194.
• Hietarinta, J., (1987), A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV- type bilinear equations, J. Math. Phys., 28(8), 1732-1742.
• Hietarinta, J., (1987), A search for bilinear equations passing Hirota’s three-soliton condition. II. mKdV-type bilinear equations, J. Math. Phys., 28(9), 2094-2101.
• Hereman, W. and Nuseir, A., (1997), Symbolic methods to construct exact solutions of nonlinear partial differential equations, Mathematics and Computers in Simulation, 43, 13-27.
• Wazwaz, A.M., (2007), Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh-coth method, Appl. Math. Comput., 190, 633-640.
• Wazwaz, A.M., (2007), Multiple-front solutions for the Burgers equation and the coupled Burgers equations, Appl. Math. Comput., 190, 1198-1206.
• Wazwaz, A.M., (2007), New solitons and kink solutions for the Gardner equation, Communications in Nonlinear Science and Numerical Simulation, 12(8), 1395-1404.
• Wazwaz, A.M., (2007), Multiple-soliton solutions for the Boussinesq equation, Appl. Math. Comput., 192, 479-486.
• Wazwaz, A.M., (2008), The Hirota’s direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation, Appl. Math. Comput., 199(1), 133-138.
• Wazwaz, A.M., (2008), Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation, Appl. Math. Comput., 200, 437-443.
• Wazwaz, A.M., (2008), Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equa- tion, Appl. Math. Comput., 201(1/2), 168-174.
• Wazwaz, A.M., (2008), The Hirota’s direct method for multiple-soliton solutions for three model equations of shallow water waves, Appl. Math. Comput., 201(1/2), 489-503.
• Wazwaz, A.M., (2008), Multiple-soliton solutions of two extended model equations for shallow water waves, Appl. Math. Comput., 201(1/2), 790-799.
• Wazwaz, A.M., (2008), Single and multiple-soliton solutions for the (2+1)-dimensional KdV equation, Appl. Math. Comput., 204, 20-26.
• Wazwaz, A.M., (2008), Solitons and singular solitons for the Gardner-KP equation, Appl. Math. Comput., 204, 162-169.
• Wazwaz, A.M., (2008), Regular soliton solutions and singular soliton solutions for the modified Kadomtsev-Petviashvili equations , Appl. Math. Comput., 204, 817-823.
• Wazwaz, A.M., (2008), Multiple kink solutions and multiple singular kink solutions for the (2+1)- dimensional Burgers equations, Appl. Math. Comput., 204, 529-541.