Open AccessOn Integration of the Loaded mKdV Equation in the Class of Rapidly Decreasing Functions
Author(s) -
А. Б. Хасанов,
AUTHOR_ID,
U. A. Hoitmetov,
AUTHOR_ID
Publication year - 2021
Publication title -
izvestiâ irkutskogo gosudarstvennogo universiteta. seriâ "matematika"/izvestiâ irkutskogo gosudarstvennogo universiteta. seria matematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.411
H-Index - 3
eISSN - 2541-8785
pISSN - 1997-7670
DOI - 10.26516/1997-7670.2021.38.19
Subject(s) - mathematics , inverse scattering transform , korteweg–de vries equation , class (philosophy) , mathematical analysis , inverse scattering problem , operator (biology) , differential equation , inverse problem , cauchy problem , initial value problem , dimension (graph theory) , inverse , mathematical physics , pure mathematics , physics , chemistry , nonlinear system , quantum mechanics , computer science , geometry , biochemistry , artificial intelligence , repressor , transcription factor , gene
The paper is devoted to the integration of the loaded modified Kortewegde Vries equation in the class of rapidly decreasing functions. It is well known that loaded differential equations in the literature are usually called equations containing in the coefficients or in the right-hand side any functionals of the solution, in particular, the values of the solution or its derivatives on manifolds of lower dimension. In this paper, we consider the Cauchy problem for the loaded modified Korteweg-de Vries equation. The problem is solved using the inverse scattering method, i.e. the evolution of the scattering data of a non-self-adjoint Dirac operator is derived, the potential of which is a solution to the loaded modified Korteweg-de Vries equation in the class of rapidly decreasing functions. A specific example is given to illustrate the application of the results obtained.