Long-time asymptotics for the focusing Hirota equation with non-zero boundary conditions at infinity via the Deift-Zhou approach

DOI10.1007/s11040-021-09388-0zbMath1477.35110arXiv2010.05376OpenAlexW3162473817WikidataQ114224697 ScholiaQ114224697MaRDI QIDQ2046709

Zhenya Yan, Bo-ling Guo, Shu-Yan Chen

Publication date: 18 August 2021

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.05376

zbMATH Keywords

long-time asymptoticsinverse scatteringfocusing Hirota equationnon-zero boundary conditionsnonlinear steepest-descent methodoscillatory Riemann-Hilbert problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Theta functions and abelian varieties (14K25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (3)

Soliton resolution for the Wadati-Konno-Ichikawa equation with weighted Sobolev initial data ⋮ Long time asymptotics for the focusing nonlinear Schrödinger equation in the solitonic region with the presence of high-order discrete spectrum ⋮ On the soliton resolution and the asymptotic stability of \(N\)-soliton solution for the Wadati-Konno-Ichikawa equation with finite density initial data in space-time solitonic regions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rarefaction waves of the Korteweg-de Vries equation via nonlinear steepest descent
• Initial-boundary value problems for integrable evolution equations with \(3\times 3\) Lax pairs
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Long-time asymptotic for the Hirota equation via nonlinear steepest descent method
• Modulation instability: The beginning
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Long-time asymptotics for the Hirota equation on the half-line
• Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions
• Long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions
• On the long time behavior of the doubly infinite Toda lattice under initial data decaying at infinity
• Focusing and defocusing Hirota equations with non-zero boundary conditions: inverse scattering transforms and soliton solutions
• Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions
• The Hirota equation: Darboux transform of the Riemann-Hilbert problem and higher-order rogue waves
• Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitons
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Long-time asymptotics for the Degasperis-Procesi equation on the half-line
• Integrable nonlinear evolution equations on a finite interval
• Bose-Einstein Condensation and Superfluidity
• Initial-Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half-Line
• The Nonlinear Steepest Descent Method: Asymptotics for Initial-Boundary Value Problems
• The nonlinear Schrödinger equation on the half-line
• The unified transform method for the Sasa–Satsuma equation on the half-line
• Focusing mKdV Breather Solutions with Nonvanishing Boundary Condition by the Inverse Scattering Method
• Nonlinear-Evolution Equations of Physical Significance
• The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions
• Focusing NLS Equation: Long-Time Dynamics of Step-Like Initial Data
• Financial Rogue Waves
• Modified KdV solitons with non-zero vacuum parameter obtainable from the ZS-AKNS inverse method
• Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions
• General Derivation of Bäcklund Transformations from Inverse Scattering Problems
• Long-time Asymptotics for the Camassa–Holm Equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Asymptotics of Solutions to the Modified Nonlinear Schrödinger Equation: Solitons on a Nonvanishing Continuous Background
• New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation
• The collisionless shock region for the long‐time behavior of solutions of the KdV equation
• A unified transform method for solving linear and certain nonlinear PDEs
• An extension of the steepest descent method for Riemann-Hilbert problems: The small dispersion limit of the Korteweg-de Vries (KdV) equation
• Method for Solving the Korteweg-deVries Equation
• Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schrödinger equation
• Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability
• An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line
• Reverse Space‐Time Nonlocal Sine‐Gordon/Sinh‐Gordon Equations with Nonzero Boundary Conditions
• Advances in the study of boundary value problems for nonlinear integrable PDEs
• Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 × 4 Lax pair on a finite interval
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
• Long‐time asymptotics of the nonlinear Schrödinger equation shock problem
• Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
• The disintegration of wave trains on deep water Part 1. Theory
• Exact envelope-soliton solutions of a nonlinear wave equation

This page was built for publication: Long-time asymptotics for the focusing Hirota equation with non-zero boundary conditions at infinity via the Deift-Zhou approach