On the complex modified Korteweg–de Vries equation with a self-consistent source and nonzero boundary conditions

Authors

DOI:

https://doi.org/10.3842/umzh.v77i1.7993

Keywords:

Inverse scattering transform, Complex modified Korteweg-de Vries equations, Zakharov-Shabat system, Self-consistent source, Non-zero boundary conditions

Abstract

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.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 1, 2025.

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Published

25.03.2025

Issue

Vol. 77 No. 1 (2025)

Section

Research articles

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Copyright (c) 2025 Anvar Reyimberganov

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Khasanov, A. B., and A. A. Reyimberganov. “On the Complex Modified Korteweg–de Vries Equation With a Self-Consistent Source and Nonzero Boundary Conditions”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 1, Mar. 2025, p. 80, https://doi.org/10.3842/umzh.v77i1.7993.