Dromion interactions of(2+1)-dimensional nonlinear evolution equations

Abstract

Starting from two line solitons, the solution of integrable (2+1)-dimensional mKdV system and KdV system in bilinear form yields a dromion solution or a "Solitoff" solution. Such a dromion solution is localized in all directions and the Solitoff solution decays exponentially in all directions except a preferred one for the physical field or a suitable potential. The interactions between two dromions and between the dromion and Solitoff are studied by the method of figure analysis for a (2+1)-dimensional modified KdV equation and a (2+1)-dimensional KdV type equation. Our analysis shows that the interactions between two dromions may be elastic or inelastic for different forms of solutions.

Interaction of Solitons in (2+1)-Dimensional Integrable Models

“…In fact, this inelastic interaction can be considered as a resonant behavior of the solution [17]. Combining the phenomena described here with results obtained by us before in [9,10,18], we ¢nd that the coupled coe¤cients a ij are not the only causes determining the interaction properties. Also the solution form of multiple line solitons is essential to decide about the interaction.…”

“…Figure 2 and 3 are interaction plots of two dromions which are formed by three ghost line solitons for the mKdV Eq. (18) and (19) with the potential w @ x 1 @ y 1 tan À1 g=f : 30…”

Interactions of dromion-like structures in the(1+1)dimension variable coefficient nonlinear Schrödinger equation

“…For the (2 + 1)-dimensional sine-Gordon equation, dromion interactions have been proven to be not elastic [16]. Moreover, dromion interactions has been elastic or inelastic for different form of solutions in (2 + 1)-dimensional KdV-type equations [17,18]. Furthermore, the dromion structure in (3 + 1) dimensions has been studied for a KdV equation [19], and dromion-like structures have been reported in the (1 + 1) dimension variable coefficient nonlinear Schrödinger (vcNLS) equation [13].…”

Dromion structures in the(2+1)-dimensional nonlinear Schrödinger equation with a parity-time-symmetric potential

“…As the nonlinear science develops, solitons have ample applications in such fields as nonlinear optics, fluid dynamics, plasma physics, condensed matter physics, solids, particle physics, astrophysics, and quantum physics [3][4][5][6][7]. Recently, dromions, as a special type of the exponentially localized soliton solutions, have attracted some attentions of physicists and mathematicians [8][9][10]. In order to study solitons including dromions, nonlinear Schrödinger (NLS) , which is one of the important nonlinear models, supplies some applications in the branches of physics [11,12].…”