Geodesic
Integration of negative-order modified Korteweg–de Vries equation with an integral source
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 63 (2024), pp. 80-90

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, it is shown that the modified Korteweg–de Vries (mKdV) equation of negative order with an integral source can be integrated by the method of the inverse spectral problem. The main result of this work is the derivation of the evolution of the spectral data of the Dirac system with a periodic potential associated with the solution of the negative-order modified Korteweg–de Vries equation with an integral source. The obtained results allow us to apply the inverse problem method to solve the negative-order modified Korteweg–de Vries equation with an integral source.
Keywords: modified Korteweg–de Vries equation of negative order, Dirac system, inverse spectral problem, Dubrovin–Trubowitz system of equations, trace formulas 
@article{IIMI_2024_63_a5,
     author = {G. U. Urazboev and M. M. Khasanov and O. B. Ismoilov},
     title = {Integration of negative-order modified {Korteweg{\textendash}de} {Vries} equation with an integral source},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {80--90},
     publisher = {mathdoc},
     volume = {63},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2024_63_a5/}
}
TY  - JOUR
AU  - G. U. Urazboev
AU  - M. M. Khasanov
AU  - O. B. Ismoilov
TI  - Integration of negative-order modified Korteweg–de Vries equation with an integral source
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2024
SP  - 80
EP  - 90
VL  - 63
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2024_63_a5/
LA  - ru
ID  - IIMI_2024_63_a5
ER  - 
%0 Journal Article
%A G. U. Urazboev
%A M. M. Khasanov
%A O. B. Ismoilov
%T Integration of negative-order modified Korteweg–de Vries equation with an integral source
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2024
%P 80-90
%V 63
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2024_63_a5/
%G ru
%F IIMI_2024_63_a5
G. U. Urazboev; M. M. Khasanov; O. B. Ismoilov. Integration of negative-order modified Korteweg–de Vries equation with an integral source. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 63 (2024), pp. 80-90. http://geodesic.mathdoc.fr/item/IIMI_2024_63_a5/