A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditions
arXiv:2203.05302 · doi:10.1007/s00605-022-01786-y
Abstract
The paper aims at developing the Riemann-Hilbert (RH) approach for the modified Camassa-Holm (mCH) equation on the line with non-zero boundary conditions, in the case when the solution is assumed to approach two different constants at different sides of the line. We present detailed properties of spectral functions associated with the initial data for the Cauchy problem for the mCH equation and obtain a representation for the solution of this problem in terms of the solution of an associated RH problem.
arXiv comment34 pages
References in corpus (18)
- An integrable shallow water equation with peaked solitons
- The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
- Dispersive shock waves and modulation theory
- Long-Time Asymptotics for the Camassa-Holm Equation
- Perturbative Symmetry Approach
- Seiberg-Witten theory as a Fermi gas
- Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data
- Rarefaction Waves of the Korteweg-de Vries Equation via Nonlinear Steepest Descent
- The focusing NLS equation with step-like oscillating background: scenarios of long-time asymptotics
- Lax integrability and the peakon problem for the modified Camassa-Holm equation
- On the isospectral problem of the dispersionless Camassa-Holm equation
- Complex oscillations in the delayed Fitzhugh-Nagumo equation
- On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations
- Bäcklund transformation and smooth multisoliton solutions for a modified Camassa-Holm equation with cubic nonlinearity
- A Riemann-Hilbert approach to the modified Camassa-Holm equation with nonzero boundary conditions
- On classical solutions of the KdV equation
- A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations
- Unique solvability of a coupling problem for entire functions