Siberian Federal University 
- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2022 15 (2)
- Authors
- Feˇckan, Michal; Urazboev, Gayrat; Baltaeva, Iroda
- Contact information
- Feˇckan, Michal: Mathematical Institute of the Slovak Academy of Sciences Bratislava, Slovakia; OCRID: 0000-0002-7385-6737; Urazboev, Gayrat: Urgench state university Urgench, Uzbekistan Institute of Mathematics, Khorezm Branch, Uzbekistan Academy of Sciences Urgench, Uzbekistan; OCRID: 0000-0002-7420-2516; Baltaeva, Iroda: Urgench, Uzbekistan Khorezm Mamun Academy Khorezm region, Khiva, Uzbekistan; OCRID: 0000-0001-5624-7529
- Keywords
- loaded modified KdV equation; inverse scattering method; "rapidly decreasing" functions; soliton; evolution of the scattering data
- 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
- Pages
- 174–183
- DOI
- 10.17516/1997-1397-2022-15-2-174-183
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/145176
Journal of Siberian Federal University. Mathematics & Physics / Inverse Scattering and Loaded Modified Korteweg-de Vries Equation
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