Scientific Research

An Academic Publisher

**Soliton Resonances of the Nonisospectral Modified Kadomtsev-Petviashvili Equation** ()

Many equations possess soliton resonances phenomenon, this paper studies the soliton resonances of the nonisospectral modified Kadomtsev-Petviashvili (mKP) equation by asymptotic analysis.

Share and Cite:

J. Yan, "Soliton Resonances of the Nonisospectral Modified Kadomtsev-Petviashvili Equation,"

*Applied Mathematics*, Vol. 2 No. 6, 2011, pp. 685-693. doi: 10.4236/am.2011.26090.Conflicts of Interest

The authors declare no conflicts of interest.

[1] | M. J. Ablowitz and P. A. Clarkson, “Solitons, Nonlinear Evolution Equations and Inverse Scattering,” Cambridge University Press, Cambridge, 1991. doi:10.1017/CBO9780511623998 |

[2] | V. B. Matveev and M. A. Salle, “Darboux Transformation and Solitons,” Springer-Verlag, Berlin, Heidelberg, 1991. |

[3] | R. Hirota, “Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons,” Physical Review Letters, Vol. 27, No. 18, November 1971, pp. 1192-1194. doi:10.1103/PhysRevLett.27.1192 |

[4] | R. Hirota, “The Direct Method in Soliton Theory,” Cambridge University Press, Cambridge, 2004. |

[5] | R. Hirota and J. Satsuma, “Nonlinear Evolution Equations Generated from the B?cklund Transformation for the Boussinesq Equation,” Progress of Theoretical Physics, Vol. 57 No. 3, September 1977, pp. 797-807. doi:10.1143/PTP.57.797 |

[6] | J. W. Miles, “Resonantly Interacting Solitary Waves,” Journal of Fluid Mechanics, Vol. 79, No. 1, April 1977, pp.171-179. doi:10.1017/S0022112077000093 |

[7] | R. Hirota and M. Ito, “Resonance of Solitons in One Dimension,” Journal of the Physical Society of Japan, Vol. 52, No. 3, August 1983, pp.744-748. doi:10.1143/JPSJ.52.744 |

[8] | M. Musette, F. Lambert and J. C. Decuyper, “Soliton and Antisoliton Resonant Interactions,” Journal of Physics A: Mathematical and General, Vol. 20, No. 18, December 1987, pp. 2207-2208. doi:10.1088/0305-4470/20/18/022 |

[9] | F. Lambert, M. Musette and E. Kesteloot, “Soliton Resonances for the Good Boussinesq Equation,” Inverse Problem, Vol. 3, No. 3, May 1987, pp. 275-288. doi:10.1088/0266-5611/3/2/010 |

[10] | K. Ohkuma and M. Wadati, “The Kadomtsev-Petviashvili Equation: The Trace Method and the Soliton Resonances,” Journal of the Physical Society of Japan, Vol. 52, No. 3, September 1983, pp. 749-760. doi:10.1143/JPSJ.52.749 |

[11] | E. Medina, “An $N$ Soliton Resonance Solution for the KP Equation: Interaction with Change of Form and Velocity,” Letters in Mathematical Physics, Vol. 62, No. 2, 2002, pp. 91-99. doi:10.1023/A:1021647025621 |

[12] | O. K. Pashaev and M. L. Y. Francisco, “Degenerate four-Virtual-Soliton Resonance for the KP-II Equation,” Theoretical and Mathematical Physics, Vol. 144, No. 1, 2005, pp. 1022-1029. doi:10.1007/s11232-005-0130-x |

[13] | G. Biondini and S. Chakravarty, “Soliton Solutions of the Kadomtsev-Petviashvili II Equation,” Journal of Mathematical Physics, Vol. 47, No. 3, February 2006, pp. 1-26. doi:10.1063/1.2181907 |

[14] | S. Isojima, R. Willox and J. Satsuma, “On Various Solutions of the Coupled KP Equation,” Journal of Physics A: Mathematical and General, Vol. 35, No. 32, May 2002, pp. 6893-6909. doi:10.1088/0305-4470/35/32/309 |

[15] | S. Isojima, R. Willox and J. Satsuma, “Spider-Web Solutions of the Coupled KP Equation,” Journal of Physics A: Mathematical and General, Vol. 36, No. 36, June 2003, pp. 9533-9552. doi:10.1088/0305-4470/36/36/307 |

[16] | J. H. Lee, R. Willox and O. K. Pashaev, “Soliton Resonances for the MKP-II,” Theoretical and Mathematical Physics, Vol. 144, No. 1, July 2005, pp. 995-1003. doi:10.1007/s11232-005-0127-5 |

[17] | H. H. Hao and D. J. Zhang, “Resonances of Line Solitons in a Non-Isospectral Kadomtsev-Petviashvili Equation,” Journal of the Physical Society of Japan, Vol. 77, April 2008, Paper ID: 045001. doi:10.1143/JPSJ.77.045001 |

[18] | L. M. Alonso, E. L. Medina and R. Hernandez, “Multidimensional Localized Coherent Structures in the Bilinear Formalism of Integrable Systems,” Inverse Problem, Vol. 7, No. 3, June 1991, p. L25. doi:10.1088/0266-5611/7/3/001 |

[19] | F. Kaka and N. Yajima, “Interaction of Ion-Acoustic Solitons in Two-Dimensional Space,” Physical Society of Japan, Vol. 49, November 1980, pp. 2063-2071. doi:10.1143/JPSJ.49.2063 |

[20] | F. Kaka and N. Yajima, “Interaction of Ion-Acoustic Solitons in Multi-Dimensional Space II,” Physical Society of Japan, Vol. 51, January 1982, pp. 311-322. doi:10.1143/JPSJ.51.311 |

[21] | Y. Zhang, S. F. Deng, D. J. Zhang and D. Y. Chen, “The N-Soliton Solutions for the Non-Isospectral Mkdv Equation,” Vol. 339, No. 3-4, August 2004, pp. 228-236. |

[22] | S. F. Deng, “The Multisoliton Solutions for the Nonisospectral mkp Equation,” Physics Letters A, Vol. 372, No. 4, January 2008, pp. 460-464. doi:10.1016/j.physleta.2007.07.060 |

[23] | Y. Zhang and Y. N. Lv, “On the Nonisospectral Modified Kadomtsev-Peviashvili Equation,” Journal of Mathematical Analysis and Applications, Vol. 342, No. 1, June 2008, pp. 534-541. doi:10.1016/j.jmaa.2007.12.032 |

Copyright © 2020 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.