Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 14 min ago
PreprintarXiv licencearXiv

A Riemann-Hilbert approach to the two-component modified Camassa-Holm system with step-like boundary conditions

  • Iryna Karpenko
  • Dmitry Shepelsky
  • Gerald Teschl
Open at sourcePDFDOICite

Abstract

We develop a Riemann--Hilbert formalism for the Cauchy problem for the two-component modified Camassa--Holm (2-mCH) system on the real line under non-zero step-like boundary conditions. Starting from the corresponding Lax pair, we carry out the direct spectral analysis and establish the analytic, symmetry, and asymptotic properties of the eigenfunctions and spectral data determined by the initial conditions. These results are then used to formulate a matrix Riemann--Hilbert problem whose solution provides a reconstruction formula for the solution of the original Cauchy problem.

Related

  1. Existence and multiplicity results for third-order ordinary differential equations with derivative dependence subject to the Riemann–Stieltjes integral boundary conditions
    Du Yue, Cui Yujun
    Demonstratio MathematicaPeer-reviewedCC BYFull textGeneral mathematicsDOAJ
  2. Ax-Schanuel and the rank one Riemann-Hilbert correspondence
    Jonathan Pila, JacobTsimerman
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Quantum Stokes matrices and quantum Riemann-Hilbert-Birkhoff maps
    Xiaomeng Xu
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  4. A prismatic Riemann-Hilbert correspondence
    Dylan Pentland
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. A Riemann-Hilbert approach to the computation of transform pairs
    Kaitlynn Lilly, Thomas Trogdon
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{karpenko2026riemannhilbert,
  title = {{A Riemann-Hilbert approach to the two-component modified Camassa-Holm system with step-like boundary conditions}},
  author = {Iryna Karpenko and Dmitry Shepelsky and Gerald Teschl},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39938},
  eprint = {2610.39938},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39938},
}
RIS
TY  - UNPB
TI  - A Riemann-Hilbert approach to the two-component modified Camassa-Holm system with step-like boundary conditions
AU  - Iryna Karpenko
AU  - Dmitry Shepelsky
AU  - Gerald Teschl
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39938
UR  - https://arxiv.org/abs/2610.39938
AB  - We develop a Riemann--Hilbert formalism for the Cauchy problem for the two-component modified Camassa--Holm (2-mCH) system on the real line under non-zero step-like boundary conditions. Starting from the corresponding Lax pair, we carry out the direct spectral analysis and establish the analytic, symmetry, and asymptotic properties of the eigenfunctions and spectral data determined by the initial conditions. These results are then used to formulate a matrix Riemann--Hilbert problem whose solution provides a reconstruction formula for the solution of the original Cauchy problem.
ER  -