On the Differential-Difference Sine-Gordon Equation with an Integral Type Source-Reference-Cited by-同舟云学术

On the Differential-Difference Sine-Gordon Equation with an Integral Type Source

Published:2023-12-01 Issue:6 Volume:73 Page:1499-1510
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Babajanov Bazar¹,Fečkan Michal²³,Babadjanova Aygul⁴

Affiliation:

1. * Urgench State UNiversity, Faculty of Physics and Mathematics , 14, H. Alimjan , Urgench , UZBEKISTAN

2. ** Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava , Mlynská dolina , Bratislava , SLOVAKIA

3. Institute of Mathematics, Slovak Academy of Sciences , Štefánikova 49 , Bratislava , SLOVAKIA

4. *** V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences , 81, str. Mirzo Ulughbek , Tashkent , UZBEKISTAN

Abstract

ABSTRACT In this work, we study the integration of the differential-difference sine-Gordon equation with an integral type source. We deduce the time performance of the scattering data of the spectral problem which is associated with the discrete sine-Gordon equation. Using the inverse scattering method, we integrate the Cauchy problem for the differential-difference sine-Gordon equation with the integral type source in the class of the rapidly decreasing functions.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2023-0108/pdf

Reference32 articles.

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2. Babajanov, B. A.—Khasanov, A. B.: Periodic Toda chain with an integral source, Theoret. Math. Phys. 184 (2015), 1114–1128.

3. Babajanov, B. A.—Fečkan, M.—Urazbaev, G. U.: On the periodic Toda lattice hierarchy with an integral source, Commun. Sci. Numer. Simul. 52 (2017), 110–123.

4. Babajanov, B. A.—Babadjanova, A. K.—Azamatov, A. S.: Integration of the differential-difference sine-Gordon equation with a self-consistent source, Theoret. Math. Phys. 210 (2022), 327–336.

5. Babadjanova, A.—Kriecherbauer, T.—Urazboev, G.: The periodic solutions of the discrete modified KdV equation with a self-consistent source, Appl. Math. Comput. 376 (2020), Art. ID 125136.

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1. Integration of the mKdV equation with time-dependent coefficients, with an additional term and with an integral source in the class of rapidly decreasing functions;Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki;2024-06