Geodesic
Integration of a~non-linear Hirota type equation with additional terms
Izvestiya. Mathematics , Tome 89 (2025) no. 1, pp. 196-219

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

In this paper, the inverse spectral problem method is used to integrate a Hirota type equation with additional terms in the class of periodic infinite-gap functions. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of six times continuously differentiable periodic infinite-gap functions is proved. It is also shown that the Cauchy problem is solvable at all times for sufficiently smooth initial conditions.
Keywords: non-linear Hirota type equation with additional terms, Dirac operator, spectral data, system of Dubrovin equations, trace formulas. 
@article{IM2_2025_89_1_a8,
     author = {A. B. Khasanov and R. Kh. Eshbekov and T. G. Hasanov},
     title = {Integration of a~non-linear {Hirota} type equation with additional terms},
     journal = {Izvestiya. Mathematics },
     pages = {196--219},
     publisher = {mathdoc},
     volume = {89},
     number = {1},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2025_89_1_a8/}
}
TY  - JOUR
AU  - A. B. Khasanov
AU  - R. Kh. Eshbekov
AU  - T. G. Hasanov
TI  - Integration of a~non-linear Hirota type equation with additional terms
JO  - Izvestiya. Mathematics 
PY  - 2025
SP  - 196
EP  - 219
VL  - 89
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2025_89_1_a8/
LA  - en
ID  - IM2_2025_89_1_a8
ER  - 
%0 Journal Article
%A A. B. Khasanov
%A R. Kh. Eshbekov
%A T. G. Hasanov
%T Integration of a~non-linear Hirota type equation with additional terms
%J Izvestiya. Mathematics 
%D 2025
%P 196-219
%V 89
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2025_89_1_a8/
%G en
%F IM2_2025_89_1_a8
A. B. Khasanov; R. Kh. Eshbekov; T. G. Hasanov. Integration of a~non-linear Hirota type equation with additional terms. Izvestiya. Mathematics , Tome 89 (2025) no. 1, pp. 196-219. http://geodesic.mathdoc.fr/item/IM2_2025_89_1_a8/