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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:2103.15373 (nlin)
[Submitted on 29 Mar 2021 (v1), last revised 4 Jun 2021 (this version, v2)]

Title:Large and infinite order solitons of the coupled nonlinear Schrödinger equation

Authors:Liming Ling, Xiaoen Zhang
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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.
Comments: 61pages, 29figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
MSC classes: 35Q55, 35Q51, 37K10, 37K15, 35Q15, 37K40
Cite as: arXiv:2103.15373 [nlin.SI]
  (or arXiv:2103.15373v2 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.2103.15373

Submission history

From: Liming Ling [view email]
[v1] Mon, 29 Mar 2021 07:00:03 UTC (1,047 KB)
[v2] Fri, 4 Jun 2021 07:49:48 UTC (1,230 KB)
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