Variable Separation and Exact Solutions for the Kadomtsev-Petviashvili Equation

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References

[1] Kadomtsev, B.B. and Petviashvili, V.I. (1970) On the Stability of Solitary Waves in Weakly Dispersive Media. Soviet Physics—Doklady, 15, 539-541.

[2] Wazwaz, A.-M. (2009) Partial Differential Equations and Solitary Waves Theory, Nonlinear Physical Science. Higher Education Press, 620-626.

[3] Ablowitz, M.J. and Clarkson, P.A. (1991) Solitons, Nonlinear Evolution Equations and inverse Scattering. Cambridge University Press, Cambridge.

http://dx.doi.org/10.1017/CBO9780511623998

[4] Liu, X.Q., Song, J. and Han, Y.Q. (2001) New Explicit Solutions to the n-Dimensional Landau-Lifshitz Equations. Physics Letter A, 281, 324-326.

[5] Zhong, P.H., Yang, R.H. and Yang, G.S. (2008) Exact Periodic and Blow up Solutions for 2D Ginzburg-Landau Equation. Physics Letters A, 373, 19-22.

[6] Evans, C. (2002) Partial Differential Equations. American Mathematical Society Providence, Rhode Island, Graduate Studies in Mathematics, Vol. 19.

[7] Qu, C.Z., Zhang, S.L. and Liu, R.C. (2000) Separation of Variables and Exact Solutions to the Quasilinear Diffusion Equations with Nonlinear Source. Physica D: Nonlinear Phenomena, 144, 97-123.

http://dx.doi.org/10.1016/S0167-2789(00)00069-5

[8] Estevez, P.G., Qu, C.Z. and Zhang, S.L. (2002) Separation of Variables of a Generalized Porous Medium Equation with Nonlinear Source. Journal of Mathematical Analysis and Applications, 275, 44-59.

http://dx.doi.org/10.1016/S0022-247X(02)00214-7

[9] Shang, Y.D. (2013) Exact Solutions for the Nonlinear Diffusion Equations with Power Law Diffusivity. Journal of Guangzhou University (Nature Science Edition), 12, 1-8.

[10] Zhang, S.L., Lou, S.Y. and Qu, C.Z. (2002) Variable Separation and Exact Solutions to Generalized Nonlinear Diffusion Equations. Chinese Physics Letters, 19, 1741-1744.

http://dx.doi.org/10.1088/0256-307X/19/12/301