Solution of the Goursat Problem for the Boussinesq–Love Equation with the Bessel Operator by the Method of Transmutation Operators.

In this paper, we use the fractional-order Erdélyi–Kober operator as a transmutation operator. Applying this operator, the formulated Goursat problem for the Boussinesq–Love equation with singular coefficients has been reduced to a similar problem for the Boussinesq–Love equation without singular coefficients. The solution to this auxiliary problem has been constructed explicitly by the Riemann method. Then, on its basis, an exact solution to the original problem is constructed. [ABSTRACT FROM AUTHOR]