On theNth Iterated Darboux Transformation and Soliton Solutions of a Coherently-Coupled Nonlinear Schrödinger System

Abstract

In this paper, we study an integrable coherently-coupled nonlinear Schrödinger system arising from low birefringent fibers and weakly anisotropic media. We construct the Nth iterated Darboux transformation (DT) in the explicit form and give a complete proof for the gauge equivalence of the associated Lax pair. By the DT-based algorithm, we derive the N-soliton solutions which can be uniformly represented in terms of the four-component Wronskians. We analyze the properties of coherently coupled solitons, revealing the parametric criterion for the non-degenerate solitons to respectively display the one-and double-hump profiles. In addition, we point out that the doublehump solitons may have potential application in realizing the multi-level optical communication.

Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium

“…[15,19] has generated the conservation laws; (4) Ref. [16] has analyzed the painlevé integrable conditions and derived some soliton solutions via the bilinear method.…”

“…The coupling effects depend on relative phases of the interacting fields, and coherent interactions usually occur when the nonlinear medium is weakly anisotropic or low birefringent [1]. And in such case, the evolution equations that govern the two orthogonally polarized components in an isotropic medium have the following normalized form [14][15][16][17][18][19] …”

Nondegenerate solitons for coupled higher-order nonlinear Schrödinger equations in optical fibers

“…In the past decade, the concept of 'nondegenerate' solitons has been pointed out in some coupled systems, such as Manakov systems [10,11], coherently coupled nonlinear Schrodinger systems [12][13][14] and long-waveshort-wave resonance interaction systems [15]. Based on the Hirota method [16], the solitons with distinct wave numbers are identified as nondegenerate solitons while the solitons with identical wave numbers are identified as degenerate solitons [17,18].…”

The Riemann-Hilbert Approach to Initial-Boundary Value Problems for Integrable Coherently Coupled Nonlinear Schrödinger Systems on the Half-Line

“…The integrability of the CCNLS systems (1.2) and (1.3) have been studied from various points of view, including works focused on Lax pairs and Painlevé property [28,33], conservation laws [39,41], solitons obtained by the bilinear method [16-18, 27-29, 33], the Darboux transformation (DT) [9], classical Jacobi elliptic functions [3] and other methods [2]. The addition, propagation and collision of solitons are analysed [18,33], the existence of multi-speed solitary wave solutions for CCNLS systems (1.2), (1.3) is established in [34] and the dynamics of non-linear waves is considered in [26].…”