Applications of Transmutations of Vekua – Erd´elyi - Lowndes Type to Differential Equations
DOI:
https://doi.org/10.52575/2687-0959-2024-56-1-27-34Keywords:
Transmutations, Vekua – Erd´elyi – Lowndes Transmutations, Composition Method, Telegraph Equation, Bessel FunctionsAbstract
In the paper we study an important class of transmutations. Transmutation theory is a well-known field of differential equations, by its methods many remarkable results on differential equations were received. We consider an important class of transmutations - Vekua-Erdelyi-Lowndes operators. These transmutations, which were introduced and studied by above mentioned mathematicians, transmute differential operators of different nature with a spectral parameter to similar operators without a spectral parameter. In particular, by this method explicit connection formulas are obtained for solutions of perturbed and unperturbed differential equations. To illustrate our results some special differential equations are considered.
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