{"title":"Multiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation","authors":"Mohammad Najafi, Ali Jamshidi","volume":60,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1964,"pagesEnd":1968,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/6076","abstract":"
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.<\/p>\r\n","references":"[1] Senthilvelan M. On the extended applications of Homogenous Balance\r\nMethod. Appl Math Comput 2001;123:381-8.\r\n[2] Li DS, Zhang HQ. New soliton-like solutions to the potential Kadomstev-\r\nPetviashvili (PKP) equation. Appl Math Comput 2003;146:381-4.\r\n[3] Mohamad Jawad AJ, Petkovic MD, Biswas A. Soliton solutions for\r\nnonlinear Calaogero-Degasperis and potential Kadomtsev-Petviashvili\r\nequations. Comput Math Appl 2011;62:2621-8.\r\n[4] Borhanifar A, Kabir MM. New periodic and soliton solutions by application\r\nof Exp-function method for nonlinear evolution equations. Journal\r\nof Computational and Applied Mathematics 2009;229:158-67.\r\n[5] Kaya D, El-Sayed SM. Numerical soliton-like solutions of the potential\r\nKadomtsevPetviashvili equation by the decomposition method. Phys Lett\r\nA 2003;320: 192-9.\r\n[6] Inan IE, Kaya D. Some exact solutions to the potential Kadomtsev-\r\nPetviashvili equation and to a system of shallow water wave equations.\r\nPhys Lett A 2006;355:314-8.\r\n[7] Hereman W, Zhaung W. Symbolic software for soliton theory. Acta\r\nApplicandae Mathematicae Phys Lett A 1980;76:95-6.\r\n[8] Hereman W, Zhuang W. A MACSYMA program for the Hirota method.\r\n13th World Congress Comput Appl Math 1991;2:842-63.\r\n[9] Hereman W, Nuseir A. Symbolic methods to construct exact solutions of\r\nnonlinear partial differential equations. Math Comput Sim 1997;43:13-\r\n27.\r\n[10] Wazwaz AM. Regular soliton solutions and singular soliton solutions\r\nfor the modified Kadomtsev-Petviashvili equations. Appl Math Comput\r\n2008;204: 817-23.\r\n[11] Wazwaz AM. A (3 + 1)-dimensional nonlinear evolution equation with\r\nmultiple soliton solutions and multiple singular soliton solutions. Appl\r\nMath Comput 2009;215:1548-52.\r\n[12] Wazwaz AM. New solitons and kink solutions for the Gardner equation.\r\nCommun Nonlinear Sci Numer Simul 2007;12:1395-404.\r\n[13] Wazwaz AM. Multiple soliton solutions for the (2 + 1)-dimensional\r\nasymmetric Nizhanik-Novikov-Veselov equation. Nonlinear Anal Ser A:\r\nTheory Meth Appl 2010;72:1314-8.\r\n[14] Pekcan A. The Hirota Direct Method (a thesis master of science). Bilkent\r\nuniversity 2005.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 60, 2011"}