On the complex modified Korteweg–de Vries equation with a self-consistent source and nonzero boundary conditions
UDC 517.957 We study the method of inverse scattering transform for defocusing complex modified Korteweg–de-Vries (cmKdV) equation with self-consistent sources (SCS) and nonzero boundary conditions at infinity. We prove a theorem on the evolution of the scattering data for a self-adjoin...
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| Datum: | 2025 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7993 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.957
We study the method of inverse scattering transform for defocusing complex modified Korteweg–de-Vries (cmKdV) equation with self-consistent sources (SCS) and nonzero boundary conditions at infinity. We prove a theorem on the evolution of the scattering data for a self-adjoint Zakharov–Shabat system in which the potential is a solution of the defocusing cmKdV equation with SCS. The obtained results enable us to solve the inverse scattering problem for the self-adjoint Zakharov–Shabat system with a potential from the class of functions nonvanishing at infinity. |
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| DOI: | 10.3842/umzh.v77i1.7993 |