The application of the method of additional argument to a system of high-order integral-differential partial differential equations is actual. Kyrgyz scientists have considered the application of this method to a system of first-order partial differential equations. In this paper, the system of integro-differential partial differential equations of the second order with initial conditions is reduced to a system of integral equations.

Topics
Integral equations, Integro-differential equation, Careers and professions
1.
A.
Ashirbaeva
,
G.
Sadykova
,
E.
Mamaziaeva
,
Zh.
Mambetov
 “
Solving of System of Partial Operator Equations of the First Order by the Method of Additional Argument
”
International Conference on Analysis and Applied Mathematics (ICAAM 2022
)
AIP Conf. Proc.
3085
,
020019
-
1
–020019-8;
https://doi.org/10.1063/5.0194796
Published by AIP Publishing.
Crossref
Search ADS
 
2.
A.
Ashirbaeva
,
G.
Sadykova
,
E.
Mamaziaeva
,
Zh.
Mambetov
 “
Construction of Solutions of Non-Linear Integro-Differential Equations of the Second Order with Derivative Under the Integral Sign
”.
Sign International Conference on Analysis and Applied Mathematics (ICAAM 2022
)
AIP Conf. Proc.
3085
,
020022
-
1
–020022-5;
https://doi.org/10.1063/5.0194797
Published by AIP Publishing.
Crossref
Search ADS
 
3.
M.I.
Imanaliev
 and
S.N.
Alekseenko
, “
On the theory of systems of nonlinear integro-differential partial differential equations of Whitham type
”, (
Reports of the Academy of Sciences
, T.
325
, No.
6
,
1992
) pp.
1111
–
1115
.
Google Scholar
 
4.
M.I.
Imanaliev
 and
S.N.
Alekseenko
, “
On the question of the existence of a smooth bounded solution for a system of two nonlinear partial differential equations of the first order
” //
Reports of the Russian Academy of Sciences
, T.
379
. No.
1
,
2001
), pp.
16
–
21
.
Google Scholar
 
5.
A. Zh.
Ashirbaeva
 and
Zh.I.
Mambetov
, “
Additional argument method for a system of nonlinear first-order partial differential equations with many variables
”, (
Science, new technologies and innovations of Kyrgyzstan
, No.
5
, Bishkek,
2017
), pp.
87
–
90
.
Google Scholar
 
6.
A. Zh.
Ashirbaeva
 and
Zh.I.
Mambetov
, “
Solution of a system of nonlinear partial differential equations of the first order with many variables
”, (
International scientific research journal
, No.
3
(
69
),
2018
), pp.
6
–
10
.
Google Scholar
 
7.
A. Zh.
Ashirbaeva
 and
G.K.
Sadykova
, “
Solution of a system of nonlinear partial differential equations with n+1 independent variables
”, (
Eurasian Scientific Association
, No.
8–1
(
78
), Moscow,
2021
), –pp.
6
–
8
.
Google Scholar
 
8.
A. Zh.
Ashirbaeva
 and
G.K.
Sadykova
, “
Solution of a system of operator partial differential equations of the first order
” (
Eurasian Scientific Association.
No.
11–1
(
81
), Moscow,
2021
), pp.
1
–
5
.
Google Scholar
 
This content is only available via PDF.
© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.