paper

Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2

arXiv:2211.04303 · doi:10.1007/s12648-023-02885-8

Abstract

We investigate the dynamics of fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2. We introduce a two-dimensional perturbation method, which generalizes the perturbation method used for studying two-pulse collisions in spatial dimension 1. We then use the generalized perturbation method to show that a fast collision in spatial dimension 2 leads to a change in the pulse shape in the direction transverse to the advection velocity vector. Moreover, we show that in the important case of a separable initial condition, the longitudinal part in the expression for the amplitude shift has a simple universal form, while the transverse part does not. Additionally, we show that anisotropy in the initial condition leads to a complex dependence of the amplitude shift on the orientation angle between the pulses. Our perturbation theory predictions are in very good agreement with results of extensive numerical simulations with the weakly perturbed diffusion-advection model. Thus, our study significantly enhances and generalizes the results of previous works on fast collisions in diffusion-advection systems, which were limited to spatial dimension 1.

arXiv commentThe paper presents a perturbation method for fast two-pulse collisions in diffusion-advection systems with weak nonlinear loss in dimension higher than 1. It generalizes the method that was used in arXiv:1702.05583 and arXiv:1808.04323 for the 1-dimensional problem. It complements the method that was presented in arXiv:2102.07438 for the high-dimensional problem in weakly nonlinear optical media

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