Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

Abstract

We systematically provide a similarity transformation reducing the (3 + 1)-dimensional inhomogeneous coupled nonlinear Schrödinger (CNLS) equation with variable coefficients and parabolic potential to the (1 + 1)-dimensional coupled nonlinear Schrödinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimensional bright-dark soliton, the interaction between two bright solitons, and the feature of the three-dimensional rogue wave with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

Periodic and rational solutions of the reduced Maxwell–Bloch equations

“…Recently, it is well known that the generation of unexpectedly huge waves (termed as "rogue waves") has received widespread attention in quite a lot of researches including oceanography, optical fields, Bose-Einstein condensates, plasma physics, etc. [9][10][11][12]. The straightforward description of a single rogue wave in mathematics is the Peregrine soliton [13], a special solution of the nonlinear Schrödinger (NLS) equation, which is a combination of the second-order rational polynomials and exponential function, and simulates the evolution of a wave of large amplitude that is localized in both space and time.…”