Research ArticleOpen AccessGoogle Scholar indexed
Soliton Resonances of the Nonisospectral Modified Kadomtsev-Petviashvili Equation
- 1
Copy link · social · email
Abstract
Many equations possess soliton resonances phenomenon, this paper studies the soliton resonances of the nonisospectral modified Kadomtsev-Petviashvili (mKP) equation by asymptotic analysis.
KeywordsSolitonResonancesHirota Bilinear MethodNonisospectral mKP Equation
- M. J. Ablowitz and P. A. Clarkson, “Solitons, Nonlinear Evolution Equations and Inverse Scattering,” Cambridge University Press, Cambridge, 1991. doi:10.1017/CBO9780511623998
- V. B. Matveev and M. A. Salle, “Darboux Transformation and Solitons,” Springer-Verlag, Berlin, Heidelberg, 1991.
- 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
- R. Hirota, “The Direct Method in Soliton Theory,” Cambridge University Press, Cambridge, 2004.
- 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
- J. W. Miles, “Resonantly Interacting Solitary Waves,” Journal of Fluid Mechanics, Vol. 79, No. 1, April 1977, pp.171-179. doi:10.1017/S0022112077000093
- 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
- 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
- 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
- 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
- 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
- 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
- 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