Periodic solutions for systems of coupled nonlinear Schrödinger equations with three and four components

Abstract

Periodic solutions for systems of coupled nonlinear Schrödinger equations (CNLS) are established by the Hirota bilinear method and elliptic functions. The interesting feature is the choice of theta functions in the formulation. The sum of moduli of the components or the total intensity of the beam in physical terms, will now be a rational function, instead of a polynomial, of elliptic functions. Each component of the CNLS may have multiple peaks within one period.

Three coupled slow temporal vector optical solitons in a cold seven-level atomic system

“…We find that real parts are indeed much larger than their relevant imaginary parts for all complex coefficients in table 1. This illustrates that equation (8) One can easy find that group velocities are not only matched but also slow. Besides, the complex coefficients in table 1 satisfy the conditions of dark solitons, which is < K U 0.…”

“…and the nonlinear coefficients U jj characterize the SPM, and To our best knowledge, equation (8) have complex coefficients and hence vector soliton solutions does not exist [29]. Actually, if the imaginary parts of these complex coefficients are much smaller than their corresponding real parts in equation (8)…”

“…During past several decades, most vector optical solitons have been reported in passive materials, i.e. glass-based optical fibers [6][7][8], in which far-off resonance driving schemes were used for avoiding optical attenuation and distortion. Owing to the lack of discrete levels and strong nonlinear effects, vector optical solitons formed in this way require strong electromagnetic fields and extended propagation distance and usually travel with a propagation velocity very close to velocity of light in vacuum.…”

Higher dimensional localized and periodic wave dynamics in a new integrable (2+1)-dimensional Kundu-Mukherjee-Naskar model

“…In this aspect, one can study the periodic nonlinear waves and hyperbolic functions (elliptic waves) which give tremendous applications in nonlinear optics, plasma physics, hydrodynamics, etc. [15,16,17,18] as they can explain many physical situations. One of the advantages of elliptic/periodic solutions is that they can be employed both for integrable as well as non-integrable evolution equations with different types of nonlinearities (for example focusing, defocussing and mixed type nonlinearities) [19,20,21,22,23,24].…”

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrödinger Equations with Multiply Components

“…The coupled nonlinear Schrödinger (CNLS) system with multiply components is an important model that has been applied to various areas of modern physics, such as optical communication, biophysics, hydrodynamics and quantum mechanics. [1−3] The CNLS equations with N c components are given by [4] i…”