Multiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation

We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

• Mohammad Najafi
• Ali Jamshidi

• Hirota bilinear method
• potential Kadomtsev-Petviashvili equation
• multiple soliton solutions
• multiple singular soliton solutions.

[1] Senthilvelan M. On the extended applications of Homogenous Balance
Method. Appl Math Comput 2001;123:381-8.
[2] Li DS, Zhang HQ. New soliton-like solutions to the potential Kadomstev-
Petviashvili (PKP) equation. Appl Math Comput 2003;146:381-4.
[3] Mohamad Jawad AJ, Petkovic MD, Biswas A. Soliton solutions for
nonlinear Calaogero-Degasperis and potential Kadomtsev-Petviashvili
equations. Comput Math Appl 2011;62:2621-8.
[4] Borhanifar A, Kabir MM. New periodic and soliton solutions by application
of Exp-function method for nonlinear evolution equations. Journal
of Computational and Applied Mathematics 2009;229:158-67.
[5] Kaya D, El-Sayed SM. Numerical soliton-like solutions of the potential
KadomtsevPetviashvili equation by the decomposition method. Phys Lett
A 2003;320: 192-9.
[6] Inan IE, Kaya D. Some exact solutions to the potential Kadomtsev-
Petviashvili equation and to a system of shallow water wave equations.
Phys Lett A 2006;355:314-8.
[7] Hereman W, Zhaung W. Symbolic software for soliton theory. Acta
Applicandae Mathematicae Phys Lett A 1980;76:95-6.
[8] Hereman W, Zhuang W. A MACSYMA program for the Hirota method.
13th World Congress Comput Appl Math 1991;2:842-63.
[9] Hereman W, Nuseir A. Symbolic methods to construct exact solutions of
nonlinear partial differential equations. Math Comput Sim 1997;43:13-
27.
[10] Wazwaz AM. Regular soliton solutions and singular soliton solutions
for the modified Kadomtsev-Petviashvili equations. Appl Math Comput
2008;204: 817-23.
[11] Wazwaz AM. A (3 + 1)-dimensional nonlinear evolution equation with
multiple soliton solutions and multiple singular soliton solutions. Appl
Math Comput 2009;215:1548-52.
[12] Wazwaz AM. New solitons and kink solutions for the Gardner equation.
Commun Nonlinear Sci Numer Simul 2007;12:1395-404.
[13] Wazwaz AM. Multiple soliton solutions for the (2 + 1)-dimensional
asymmetric Nizhanik-Novikov-Veselov equation. Nonlinear Anal Ser A:
Theory Meth Appl 2010;72:1314-8.
[14] Pekcan A. The Hirota Direct Method (a thesis master of science). Bilkent
university 2005.