Abstract:
We propose a method for solving the (2+1)-dimensional Kadomtsev–Petviashvili equation with negative dispersion (KP-II) using the second and third members of the disipative version of the AKNS hierarchy. We show that dissipative solitons (dissipatons) of those members yield the planar solitons of the KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for the KP-II, by which we construct one- and two-soliton solutions and study the resonance character of their mutual interactions. Using our bilinear form, for the first time, we create a four-virtual-soliton resonance solution of the KP-II, and we show that it can be obtained as a reduction of a four-soliton solution in the Hirota–Satsuma bilinear form for the KP-II.
Citation:
O. K. Pashaev, L. Y. Francisco, “Degenerate Four-Virtual-Soliton Resonance for the KP-II”, TMF, 144:1 (2005), 162–170; Theoret. and Math. Phys., 144:1 (2005), 1022–1029