A nonlocal nonlinear Schrodinger equation derived from a two-layer fluid model

Abstract

By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then a general form of nonlocal nonlinear Schrodinger (NNLS) equation with shifted parity, charge-conjugate and delayed time reversal is obtained by using multi-scale expansion method. Some kinds of elliptic periodic wave solutions of the NNLS equation are obtained by using function expansion method, which contain soliton solutions and kink solutions when the modulus taking as unity. Some representative figures of these solutions are given and analyzed in detail. In addition, by carrying out the classical symmetry method on the NNLS equation, not only the Lie symmetry group but also the related symmetry reduction solutions are given.

References in corpus (6)

• Observation of optical spatial solitons in a highly nonlocal medium
• Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
• Matter-wave dark solitons: stochastic vs. analytical results
• Exact $P_s{T}_d$ Invariant and $P_s{T}_d$ Symmetric Breaking solutions, Symmetry Reductions and Bäcklund Transformations For An AB-KdV System
• Coherent structure of Alice-Bob modified Korteweg de-Vries Equation
• Quasiperiodic oscillations and homoclinic orbits in the nonlinear nonlocal Schrödinger equation