Resonant collisions among diverse solitary waves of the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation
Lin Jiang, Xin Li, Biao Li
Abstract
Abstract According to N -soliton solutions generated by the Hirota’s bilinear method, the resonant collisions among diverse solitary waves can be obtained when the phase shifts of involved solitary waves tend to infinity. Under this constraint, the resonant collisions among a lump and dark line solitons can be derived from that of a breather and dark line solitons by means of an ingenious limiting approach. This paper takes the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> -dimensional asymmetrical Nizhnik-Novikov-Veselov equation as an example to introduce how to utilize this constraint to derive the resonant collisions among different solitary waves containing breather, lump and dark line solitons in detail. At the same time, the dynamic behaviors of the interacting waveforms are exhibited visually by some figures which include intriguing phenomena. And the characteristics and properties of these interacting waveforms are discussed. In terms of feasibility and practicability, the procedures of analysis in this paper can be exploited widely to study resonant collisions of different waveforms in other integrable systems. The results obtained would enhance the completeness of nonlinear localized wave theory.