Abstract
In this review, we present an integral transform that maps solutions of some class of the partial differential equations with time-independent coefficients to solutions of more complicated equations, which have time-dependent coefficients. We illustrate this transform by applications to model equations. In particular, we give applications to the Klein–Gordon and wave equations in the curved spacetimes such as the de Sitter universe.
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Acknowledgements
This paper was completed during my visit at the Technical University Bergakademie Freiberg in the summer of 2016. I am grateful to Michael Reissig for the invitation to Freiberg and for the warm hospitality. I express my gratitude to the Deutsche Forschungsgemeinschaft for the financial support under the grant GZ: RE 961/21-1.
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Yagdjian, K. (2018). Integral Transform Approach to Solving Klein–Gordon Equation with Variable Coefficients. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_49
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