Riemann–Hilbert approach to the focusing and defocusing nonlocal complex modified Korteweg–de Vries equation with step-like initial data

DOI10.1063/5.0174719OpenAlexW4391377851WikidataQ128946086 ScholiaQ128946086MaRDI QIDQ6188567

Publication date: 7 February 2024

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/5.0174719

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Riemann-Hilbert problems in context of PDEs (35Q15)

Cites Work

Unnamed Item
On the Darboux matrices of Bäcklund transformations for AKNS systems
An initial-boundary value problem on the half-line for the MKdV equation
On a Riemann-Hilbert problem for the Fokas-Lenells equation
Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies
On a nonlocal modified Korteweg-de Vries equation: integrability, Darboux transformation and soliton solutions
On a Riemann-Hilbert problem for the focusing nonlocal mKdV equation with step-like initial data
Asymptotic stage of modulation instability for the nonlocal nonlinear Schrödinger equation
Type \(( - \lambda, - \lambda^\ast)\) reduced nonlocal integrable mKdV equations and their soliton solutions
Nonlocal integrable mKdV equations by two nonlocal reductions and their soliton solutions
\( \overline{\partial} \)-dressing method for the nonlocal mKdV equation
The initial-boundary value problems of the new two-component generalized Sasa-Satsuma equation with a \(4\times 4\) matrix Lax pair
On the Riemann-Hilbert problem of the Kundu equation
Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system
Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data
Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions
On the Riemann-Hilbert problem for the mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation
The Hirota equation: Darboux transform of the Riemann-Hilbert problem and higher-order rogue waves
The soliton solutions for the Wadati-Konno-Ichikawa equation
Riemann-Hilbert approach for an initial-boundary value problem of the two-component modified Korteweg-de Vries equation on the half-line
A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform
On the Riemann-Hilbert problem for the integrable three-coupled Hirota system with a \(4 \times 4\) matrix Lax pair
A Class of Exactly Solvable Nonlinear Evolution Equations
The Modified Korteweg-de Vries Equation
Long-Time Asymptotics for the Nonlocal MKdV Equation*
Generalised KdV and MKdV equations associated with symmetric spaces
Integrable Nonlocal Nonlinear Equations
General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
THE mKdV EQUATION ON THE HALF-LINE
Curved wedges in the long‐time asymptotics for the integrable nonlocal nonlinear Schrödinger equation
Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation
Exact envelope-soliton solutions of a nonlinear wave equation
Reduced nonlocal integrable mKdV equations of type (−λ, λ) and their exact soliton solutions

This page was built for publication: Riemann–Hilbert approach to the focusing and defocusing nonlocal complex modified Korteweg–de Vries equation with step-like initial data