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

  • Bazar Babajanov , Michal Fečkan EMAIL logo and Aygul Babadjanova
Published/Copyright: December 18, 2023
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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.

2020 Mathematics Subject Classification: 34L25; 34K08; 34K29; 37K15

(Communicated by Jozef Džurina)


Acknowledgement

This work is partially supported by the Slovak Grant Agency VEGA No. 2/0127/20 and No. 1/0084/23 and the Slovak Research and Development Agency under the contract No. APVV-18-0308.

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Received: 2022-12-12
Accepted: 2023-02-20
Published Online: 2023-12-18

© 2023 Mathematical Institute Slovak Academy of Sciences

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