The Cauchy Problem for the Nonlinear Complex Modified Korteweg-de Vries Equation with Additional Terms in the Class of Periodic Infinite-Gap Functions

We use the inverse spectral problem method for integrating the nonlinear complex modified Korteweg-de Vries equation (cmKdV) with additional terms in the class of periodic infinite-gap functions. Also, we deduce the evolution of the spectral data of the periodic Dirac operator whose coefficient is a...

Full description

Saved in:
Bibliographic Details
Published inSiberian mathematical journal Vol. 65; no. 4; pp. 846 - 868
Main Authors Khasanov, A. B., Khasanov, T. G.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2024
Springer Nature B.V
Subjects
Cauchy problems
Differential equations
Korteweg-Devries equation
Mathematics
Mathematics and Statistics
Operators (mathematics)
spectral data
system of Dubrovin differential equations
trace formulas
Dirac operator
517.957
complex modified Korteweg-de Vries equation
Online AccessGet full text

Cover

More Information
Summary:We use the inverse spectral problem method for integrating the nonlinear complex modified Korteweg-de Vries equation (cmKdV) with additional terms in the class of periodic infinite-gap functions. Also, we deduce the evolution of the spectral data of the periodic Dirac operator whose coefficient is a solution to cmKdV. We prove that the Cauchy problem is solvable for an infinite system of Dubrovin differential equations in the class of six times continuously differentiable periodic infinite-gap functions. Moreover, we establish the solvability of the Cauchy problem for cmKdV with additional terms in the class of six times continuously differentiable periodic infinite-gap functions.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446624040128