Explicit solutions of Cauchy problems for degenerate hyperbolic equations with Transmutations methods

‎This article's primary goal is to compute an explicit transmutation-based solution to a degenerate hyperbolic equation of second order in terms of time‎. ‎To reduce a new problem to a problem that has already been solved‎, ‎or at the very least to a smaller problem‎, ‎is a standard mathematics strategy known as the transmutations method‎. ‎similar to utilizing heat equations to solve wave equations‎. ‎Using transmutation methods‎, ‎we solve this problem using the well-known Kolmogorov equation‎. We present the solution of wave equations using transmutation methods and show that it is equivalent to the solution obtained by applying the Fourier transform in order to support our methodology‎.

Keywords:

Degenerate Partial Differential Equations , Transmutation Methods , Kolmogorov Equation , Inverse Laplace transform , Laplace Transform