Affiliation:
1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract
Abstract
Variable-coefficient nonlinear Schrödinger (NLS)-type models are used to describe certain phenomena in plasma physics, nonlinear optics, arterial mechanics, and Bose–Einstein condensation. In this article, the coupled variable-coefficient cubic-quintic NLS equations with external potentials in the non-Kerr fibre are investigated. Via symbolic computation, similarity transformations and relevant constraints on the coefficient functions are obtained. Based on those transformations, such equations are transformed into the coupled cubic-quintic NLS equations with constant coefficients. Nonautonomous soliton solutions are derived, and propagation and interaction of the nonautonomous solitons in the non-Kerr fibre are investigated analytically and graphically. Those soliton solutions are related to the group velocity dispersion r(x) and external potentials h
1(x) and h
2(x, t). With the different choices of r(x), parabolic, cubic, and periodically oscillating solitons are obtained; with the different choices of h
2(x, t), we can see the dromion-like structures and nonautonomous solitons with smooth step-like oscillator frequency profiles, to name a few.
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics
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