Far-field asymptotics for multiple-pole solitons in the large-order limit

DOI10.1016/j.jde.2021.06.016zbMath1473.35497arXiv1911.04327OpenAlexW3173893198MaRDI QIDQ2042680

Deniz Bilman, Deng-Shan Wang, Robert J. Buckingham

Publication date: 21 July 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.04327

zbMATH Keywords

nonlinear Schrödinger equationsoliton solutionsRiemann-Hilbert problems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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Uses Software

• DLMF
• rogue-waves

Cites Work

• Unnamed Item
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• Cauchy-type determinants and integrable systems
• Multiple pole solutions of the nonlinear Schrödinger equation
• Limits of soliton solutions
• On the increasing tritronquée solutions of the Painlevé-II equation
• Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy
• Rational solutions of the Painlevé-III equation: large parameter asymptotics
• Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• A non-abelian nonlinear Schrödinger equation and countable superposition of solitons
• Large-degree asymptotics of rational Painlevé-II functions: noncritical behaviour
• The noncommutative AKNS system: projection to matrix systems, countable superposition and soliton-like solutions
• TheN-soliton of the focusing nonlinear Schrödinger equation forN large
• Asymptotics for the multiple pole solutions of the nonlinear Schrödinger equation
• The regularity of the multiple higher‐order poles solitons of the NLS equation
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation

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