A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditions
From MaRDI portal
Publication:2699871
DOI10.1007/s00605-022-01786-yOpenAlexW4303433033MaRDI QIDQ2699871
I. Karpenko, Gerald Teschl, Dimitry Shepelsky
Publication date: 19 April 2023
Published in: Monatshefte für Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.05302
Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) 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)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Asymptotics of step-like solutions for the Camassa-Holm equation
- Rarefaction waves of the Korteweg-de Vries equation via nonlinear steepest descent
- Stability of peakons for an integrable modified Camassa-Holm equation with cubic nonlinearity
- Oscillation-induced blow-up to the modified Camassa-Holm equation with linear dispersion
- The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
- Long time asymptotics of the Camassa-Holm equation on the half-line
- On a class of physically important integrable equations
- Solutions of the Korteweg-de Vries equation with steplike initial data
- The Camassa-Holm hierarchy, \(N\)-dimensional integrable systems, and algebro-geometric solution on a symplectic submanifold
- The modified Camassa-Holm equation in Lagrangian coordinates
- Hamiltonian structure of peakons as weak solutions for the modified Camassa-Holm equation
- Lax integrability and the peakon problem for the modified Camassa-Holm equation
- Matrix Riemann-Hilbert problems with jumps across Carleson contours
- Unique solvability of a coupling problem for entire functions
- On a new two-component \(b\)-family peakon system with cubic nonlinearity
- A few remarks on the Camassa-Holm equation.
- Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
- On the isospectral problem of the dispersionless Camassa-Holm equation
- Wave-breaking and peakons for a modified Camassa-Holm equation
- Existence of permanent and breaking waves for a shallow water equation: a geometric approach
- Dispersive shock waves and modulation theory
- Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions
- The focusing NLS equation with step-like oscillating background: the genus \(3\) sector
- On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data. II: Perturbations with finite moments
- Riemann-Hilbert problem for Camassa-Holm equation with step-like initial data
- A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
- The short pulse equation by a Riemann-Hilbert approach
- On the Cauchy problem for the integrable modified Camassa-Holm equation with cubic nonlinearity
- The algebro-geometric solutions for the Fokas-Olver-Rosenau-Qiao (FORQ) hierarchy
- The focusing NLS equation with step-like oscillating background: scenarios of long-time asymptotics
- Soliton asymptotics for the KdV shock problem via classical inverse scattering
- On the weak solutions to a shallow water equation
- A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations
- Orbital stability of peakons for a generalization of the modified Camassa–Holm equation
- The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions
- Regularization of a sharp shock by the defocusing nonlinear Schrödinger equation
- Painlevé-Type Asymptotics for the Camassa–Holm Equation
- A new integrable equation with cuspons and W/M-shape-peaks solitons
- Long-time Asymptotics for the Camassa–Holm Equation
- On the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial data: I. Schwartz-type perturbations
- Generalizations of the Camassa–Holm equation
- Inverse scattering on the line
- Perturbative symmetry approach
- An integrable shallow water equation with peaked solitons
- Camassa–Holm, Korteweg–de Vries and related models for water waves
- Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability
- The correspondence between KdV and Camassa-Holm
- Inverse scattering transform for the focusing nonlinear Schrödinger equation with counterpropagating flows
- The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem
- On classical solutions of the KdV equation
- A Riemann–Hilbert approach to the modified Camassa–Holm equation with nonzero boundary conditions
- On the blow-up of solutions to the integrable modified Camassa–Holm equation
- The Ostrovsky–Vakhnenko equation by a Riemann–Hilbert approach
- Liouville Integrability of Conservative Peakons for a Modified CH equation
- A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
- Zero curvature formulations of dual hierarchies
- Long‐time asymptotics of the nonlinear Schrödinger equation shock problem
- Long-time asymptotics for the Korteweg–de Vries equation with step-like initial data
- Bäcklund transformation and smooth multisoliton solutions for a modified Camassa-Holm equation with cubic nonlinearity
- The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula
- Analysis on the blow-up of solutions to a class of integrable peakon equations
- Liouville correspondence between the modified KdV hierarchy and its dual integrable hierarchy
This page was built for publication: A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditions
