Article

Inverse Scattering and Loaded Modified Korteweg-de Vries Equation

Michal FeˇckanInstitute of Mathematics, Khorezm Branch, Uzbekistan Academy of Sciences Urgench, Uzbekistan

Journal of Siberian Federal University Mathematics & Physicsjournal2022en

ABI

Abstract

The Cauchy problem for the loaded modified Korteweg-de Vries equation in the class of "rapidly decreasing" functions is considered in this paper. The main result of this work is a theorem on the evolution of the scattering data of the Dirac operator. Potential of the operator is the solution to the loaded modified Korteweg-de Vries equation. The obtained equalities allow one to apply the method of the inverse scattering transform to solve the Cauchy problem for the loaded modified Korteweg-de Vries equation

Topics

Differential Equations and Boundary Problems Numerical methods in inverse problems Differential Equations and Numerical Methods

Identifiers

DOI: 10.17516/1997-1397-2022-15-2-174-183

Citations and references

Cited by 2 9 references

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