论文信息 - The Kadomtsev-Petviashvili Equation: the Trace Method and the Soliton Resonances

The Kadomtsev-Petviashvili Equation: the Trace Method and the Soliton Resonances

The trace method which has been proposed by one of the authors (M.W.) and Sawada is applied to the Kadomtsev-Petviashvili equation with negative dispersion. The N-soliton solution and the Gelfand-Levitan equation are derived through the trace method. Soliton resonances are studied. It is found that the soliton resonance occurs when a virtual soliton in soliton solution turns into exact 1-soliton. Furthermore some interesting examples of soliton resonance related to 3-soliton solution are pointed out.

Kenji Ohkuma | M. Wadati | Miki Wadati | K. Ohkuma

[1] H. Ikezi,et al. Two-Dimensional Interaction of Ion-Acoustic Solitons , 1980 .

[2] John W. Miles,et al. Obliquely interacting solitary waves , 1977, Journal of Fluid Mechanics.

[3] Morikazu Toda,et al. The Exact N-Soliton Solution of the Korteweg-de Vries Equation , 1972 .

[4] Vladimir E. Zakharov,et al. A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I , 1974 .

[5] M. Wadati,et al. NEW REPRESENTATIONS OF THE SOLITON SOLUTION FOR THE KORTEWEG-DE VRIES EQUATION , 1980 .

[6] Junkichi Satsuma,et al. N-Soliton Solution of the Two-Dimensional Korteweg-deVries Equation , 1976 .

[7] Alan C. Newell,et al. Breakdown of Zakharov-Shabat theory and soliton creation , 1977 .

[8] Fujio Kako,et al. Interaction of ion-acoustic solitons in two-dimensional space , 1978 .