Classification of Single Traveling Wave Solutions to the Generalized Kadomtsev-Petviashvili Equation without Dissipation Terms in *p* = 2

ABSTRACT

By using the complete discrimination system for the polynomial method, the classification of single traveling wave solutions to the generalized Kadomtsev-Petviashvili equation without dissipation terms in *p*=2 is obtained.

Cite this paper

X. Du and H. Xin, "Classification of Single Traveling Wave Solutions to the Generalized Kadomtsev-Petviashvili Equation without Dissipation Terms in*p* = 2," *Advances in Pure Mathematics*, Vol. 3 No. 9, 2013, pp. 1-8. doi: 10.4236/apm.2013.39A1001.

X. Du and H. Xin, "Classification of Single Traveling Wave Solutions to the Generalized Kadomtsev-Petviashvili Equation without Dissipation Terms in

References

[1] M. J. Ablowits, “Lectures on the Inverse Scattering Transform,” Studies in Applied Mathematics, Vol. 58, No. 11, 1978, pp. 17-94.

[2] G. C. Das and J. Sarma, “Evolution of Solitary Waves in Multicomponent Plasmas,” Chaos, Solitons and Fractals, Vol. 9, No. 6, 1998, pp. 901-911. http://dx.doi.org/10.1016/S0960-0779(97)00170-7

[3] X. Zhao, W. Xu, H. Jia and H. Zhou, “Solitary Wave Solutions for the Modified Kadomtsev-Petvisahvili Equation,” Chaos, Solitons, and Fractals, Vol. 74, 2007, pp. 465-475. http://dx.doi.org/10.1016/j.chaos.2006.03.046

[4] W. X. Ma, A. Abdeljabbar and M. G. Assad, “Wronskian and Grammian Solutions to a (3 + 1)-Dimensional Generalized KP Equation,” Applied Mathematics and Computation, Vol. 217, No. 24, 2011, pp. 10016-10023. http://dx.doi.org/10.1016/j.amc.2011.04.077

[5] A. M. Wazwaz, “Multiple-Soliton Solutions for a (3 + 1)-Dimensional Generalized KP Equation,” Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 2, 2012, pp. 491-495. http://dx.doi.org/10.1016/j.cnsns.2011.05.025

[6] W. X. Ma and A. Abdeljabbar, “A Bilinear Backlund Transformation of a (3 + 1)-Dimensional Generalized KP Equation,” Applied Mathematics Letters, Vol. 25, No. 10, 2012, pp. 1500-1504. http://dx.doi.org/10.1016/j.aml.2012.01.003

[7] G. B. Whitham, “Linear and Nonlinaer Wave,” John Wiley, New York, 1974.

[8] W. Hereman and A. Nuseir, “Symbolic Methods to Construct Exact Solutions of Nonlinear Partial Differential Equations,” Mathematics and Computers in Simulation, Vol. 43, No. 1, 1997, pp. 13-27. http://dx.doi.org/10.1016/S0378-4754(96)00053-5

[9] W. X. Ma and A. Pekcan, “Uniqueness of the Kadomtsev-Petviashvili and Boussinesq Equations,” Zeitschrift für Naturforschung A, Vol. 66, 2011, pp. 377-382.

[10] C. S. Liu, “Applications of complete Discrimination System for Polynomial for Classifications of Traveling Wave Solutions to Nolinear Differential Equations,” Computer Physics Communications, Vol. 181, No. 2, 2010, pp. 317-324. http://dx.doi.org/10.1016/j.cpc.2009.10.006

[11] C. S. Liu, “Classification of All Single Traveling Wave Solutions to Calogero-Focas Equation,” Communications in Theoretical Physics, Vol. 48, 2007, pp. 601-604. http://dx.doi.org/10.1088/0253-6102/48/4/004

[12] C. S. Liu, “Exact Traveling Wave Solutions for (1 + 1)-Dimentional Dispersive Long Wave Equation,” Chinese Physical Society, Vol. 14, No. 9, 2005, pp. 1710-1716.

[13] C. S. Liu, “Direct Integral Method, Complete Discrimination System for Polynomial and Applications to Classifications of All Single Traveling Wave Solutions to Nonlinear Differential Equations: A Survey,” arXiv:nlin/ 0609058v1, 2006.

[1] M. J. Ablowits, “Lectures on the Inverse Scattering Transform,” Studies in Applied Mathematics, Vol. 58, No. 11, 1978, pp. 17-94.

[2] G. C. Das and J. Sarma, “Evolution of Solitary Waves in Multicomponent Plasmas,” Chaos, Solitons and Fractals, Vol. 9, No. 6, 1998, pp. 901-911. http://dx.doi.org/10.1016/S0960-0779(97)00170-7

[3] X. Zhao, W. Xu, H. Jia and H. Zhou, “Solitary Wave Solutions for the Modified Kadomtsev-Petvisahvili Equation,” Chaos, Solitons, and Fractals, Vol. 74, 2007, pp. 465-475. http://dx.doi.org/10.1016/j.chaos.2006.03.046

[4] W. X. Ma, A. Abdeljabbar and M. G. Assad, “Wronskian and Grammian Solutions to a (3 + 1)-Dimensional Generalized KP Equation,” Applied Mathematics and Computation, Vol. 217, No. 24, 2011, pp. 10016-10023. http://dx.doi.org/10.1016/j.amc.2011.04.077

[5] A. M. Wazwaz, “Multiple-Soliton Solutions for a (3 + 1)-Dimensional Generalized KP Equation,” Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 2, 2012, pp. 491-495. http://dx.doi.org/10.1016/j.cnsns.2011.05.025

[6] W. X. Ma and A. Abdeljabbar, “A Bilinear Backlund Transformation of a (3 + 1)-Dimensional Generalized KP Equation,” Applied Mathematics Letters, Vol. 25, No. 10, 2012, pp. 1500-1504. http://dx.doi.org/10.1016/j.aml.2012.01.003

[7] G. B. Whitham, “Linear and Nonlinaer Wave,” John Wiley, New York, 1974.

[8] W. Hereman and A. Nuseir, “Symbolic Methods to Construct Exact Solutions of Nonlinear Partial Differential Equations,” Mathematics and Computers in Simulation, Vol. 43, No. 1, 1997, pp. 13-27. http://dx.doi.org/10.1016/S0378-4754(96)00053-5

[9] W. X. Ma and A. Pekcan, “Uniqueness of the Kadomtsev-Petviashvili and Boussinesq Equations,” Zeitschrift für Naturforschung A, Vol. 66, 2011, pp. 377-382.

[10] C. S. Liu, “Applications of complete Discrimination System for Polynomial for Classifications of Traveling Wave Solutions to Nolinear Differential Equations,” Computer Physics Communications, Vol. 181, No. 2, 2010, pp. 317-324. http://dx.doi.org/10.1016/j.cpc.2009.10.006

[11] C. S. Liu, “Classification of All Single Traveling Wave Solutions to Calogero-Focas Equation,” Communications in Theoretical Physics, Vol. 48, 2007, pp. 601-604. http://dx.doi.org/10.1088/0253-6102/48/4/004

[12] C. S. Liu, “Exact Traveling Wave Solutions for (1 + 1)-Dimentional Dispersive Long Wave Equation,” Chinese Physical Society, Vol. 14, No. 9, 2005, pp. 1710-1716.

[13] C. S. Liu, “Direct Integral Method, Complete Discrimination System for Polynomial and Applications to Classifications of All Single Traveling Wave Solutions to Nonlinear Differential Equations: A Survey,” arXiv:nlin/ 0609058v1, 2006.