Integration of the modified Korteweg-de Vries equation with an integral source
https://doi.org/10.22405/2226-8383-2026-27-1-111-133
Abstract
In this paper, we consider the modified Korteweg–de Vries equation with an integral source.
It is shown that the inverse spectral problem method can be applied to integrate the modified Korteweg–de Vries equation with an integral source. The evolution of the spectral data of the Dirac operator with a periodic potential associated with the solution of the modified
Korteweg–de Vries equation with an integral source is determined. The solvability of the Cauchy problem for the infinite system of Dubrovin–Trubowitz differential equations in the class of six times continuously differentiable periodic functions is proved. It is shown that the constructed solution, indeed, satisfies the equation under consideration.
About the Authors
Alisher Bekchanovich Yaxshimuratov
Mamun University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Muzaffar Masharipovich Khasanov
Urgench State University
Russian Federation
Russian Federation
doctor of philosophy (PhD) in physical and mathematical sciences
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Review
For citations:
Yaxshimuratov A.B., Khasanov M.M. Integration of the modified Korteweg-de Vries equation with an integral source. Chebyshevskii Sbornik. 2026;27(1):111-133. (In Russ.) https://doi.org/10.22405/2226-8383-2026-27-1-111-133
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