Large and infinite order solitons of the coupled nonlinear Schrödinger equation

Abstract

We study the large order and infinite order soliton of the coupled nonlinear Schrodinger equation with the Riemann-Hilbert method. By using the Riemann-Hilbert representation for the high order Darboux dressing matrix, the large order and infinite order solitons can be analyzed directly without using inverse scattering transform. We firstly disclose the asymptotics for large order soliton, which is divided into four different regions -- the elliptic function region, the non-oscillatory region, the exponential and algebraic decay region. We verify the consistence between asymptotic expression and exact solutions by the Darboux dressing method numerically. Moreover, we consider the property and dynamics for infinite order solitons -- a special limitation for the larger order soliton. It is shown that the elliptic function and exponential region will disappear for the infinite order solitons.

arXiv comment61pages, 29figures

References in corpus (7)

• Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates
• Financial Rogue Waves Appearing in the Coupled Nonlinear Volatility and Option Pricing Model
• Inelastic Collision and Switching of Coupled Bright Solitons in Optical Fibers
• Akhmediev breathers, Ma solitons and general breathers from rogue waves: A case study in Manakov system
• Nondegenerate solitons in Manakov system
• Non-degenerate Bound State Solitons in Multi-component Bose-Einstein Condensates
• On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System

Cited by in corpus (3)

• Darboux transformation and solitonic solution to the coupled complex short pulse equation
• Kadomtsev-Petviashvili equation: one-constraint method and lump pattern
• Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type