The soliton solutions, dromions of the Kadomtsev–Petviashvili and Jimbo–Miwa equations in (3 + 1)-dimensions

Abstract By applying the Painleve test, the Kadomtsev–Petviashvili equation and Jimbo–Miwa equation in (3 + 1)-dimensions are shown to be non-integrable. Through the obtained truncated Painleve expansions, two bilinear equations are constructed. In addition, starting from the bilinear equations, one soliton, two soliton and dromion solutions are also derived. The analysis of the dromions shows that the interactions of the dromions for the (3 + 1)-dimensional equations may be elastic or inelastic.

[1]  Yi-Xin Chen,et al.  Dromion Interactions of (2+1)-Dimensional KdV-type Equations , 2003 .

[2]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[3]  K. Porsezian,et al.  Painlevé analysis and Bäcklund transformation for a three-dimensional Kadomtsev-Petviashvili equation , 1997 .

[4]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .

[5]  J. A. E. R. Institute,et al.  N soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3 1) dimensions , 1998, solv-int/9801003.

[6]  J. Leon,et al.  Scattering of localized solitons in the plane , 1988 .

[7]  C. Gu,et al.  Soliton theory and its applications , 1995 .

[8]  R. Hirota.  Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[9]  Alfred Ramani,et al.  Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable? , 1986 .

[10]  R. Radha,et al.  Singularity analysis and localized coherent structures in (2+1)‐dimensional generalized Korteweg–de Vries equations , 1994 .

[11]  M. Wadati,et al.  Relationships among Inverse Method, Bäcklund Transformation and an Infinite Number of Conservation Laws , 1975 .

[12]  M. Boiti,et al.  On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions , 1986 .

[13]  S. Lou.  Generalized dromion solutions of the (2+1)-dimensional KdV equation , 1995 .

[14]  Zhibin Li,et al.  Exact travelling wave solutions of the Whitham–Broer–Kaup and Broer–Kaup–Kupershmidt equations , 2005 .

[15]  M. Tabor,et al.  The Painlevé property for partial differential equations , 1983 .

[16]  Hon-Wah Tam,et al.  SOLITON SOLUTIONS TO THE JIMBO-MIWA EQUATIONS AND THE FORDY-GIBBONS-JIMBO-MIWA EQUATION , 1999 .

[17]  M. Wadati,et al.  Simple Derivation of Bäcklund Transformation from Riccati Form of Inverse Method , 1975 .

[18]  Zhi-bin Li,et al.  Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple , 2004, Comput. Phys. Commun..

[19]  Senatorski,et al.  Simulations of Two-Dimensional Kadomtsev-Petviashvili Soliton Dynamics in Three-Dimensional Space. , 1996, Physical review letters.

[20]  R. Hirota,et al.  Multidromion solutions to the Davey-Stewartson equation , 1990 .

[21]  The study of dromion interactions of (2+1)-dimensional integrable systems , 1999 .

[22]  Yinping Liu,et al.  A Maple package for finding exact solitary wave solutions of coupled nonlinear evolution equations , 2003 .

[23]  J. Hietarinta.  One-dromion solutions for genetic classes of equations , 1990 .