Transport of Nonautonomous Solitons in Two‐Dimensional Disordered Media

Abstract

Transport of localized nonlinear excitations in disordered media is an interesting and important topic in modern physics. Investigated in this work is transport of two-dimensional (2D) solitons for a nonlinear Schrödinger equation with inhomogeneous nonlocality and disorder. We use the variational method to show that, the shape (size) of solitons can be manipulated through adjusting the nonlocality, which, in turn, affects the soliton mobility. Direct numerical simulations reveal that the influence of disorder on the soliton transport accords with our analysis by the variational method. Besides, we have demonstrated an anisotropic transport of the 2D nonautonomous solitons as well. Our study is expected to shed light on modulating solitons through material properties for specifying their transport in disordered media.

Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics

“…Substituting the linear relation Φ n (z) � a(z)Ψ n (z) + b(z)Ψ n (z) into equation (37) and setting n ⟶ +∞ yields…”

“…Recently, some new analytical approaches [16][17][18][19][20][21][22][23][24][25], novel nonlinear results [26][27][28][29][30][31][32][33][34], and soliton dynamics in inhomogeneous media [35][36][37] for differential equations have been reported. Generally speaking, extending the existing methods for differential equations encounters the difficulty in searching for the iterative relations of discrete variables.…”

More “Critical Mass”, Higher Quality and Visibility of Annalen der Physik

“…The present regular issue of Annalen der Physik is a perfect example for the successful path that the journal has taken over the past five years: It contains two Rapid Research Letters on soliton transport and aperiodic photonic crystals, one Review Article by Pedro David Garcia and Peter Lodahl on quantum photonics, and two Feature Articles by Sandro Wimberger et al . and David M. Weld et al ,.…”