A Cauchy Problem for the Boussinesq–Love Equation with the Bessel Operator

The article investigates the Cauchy problem for the Boussinesq–Love equation with the Bessel operator. The problem is solved using the Riemann method. The Erdélyi–Kober transmutation operator is applied to construct the Riemann function. The Riemann function for this equation is derived, which is expressed in terms of hypergeometric functions. In particular, the Riemann function for the one-dimensional Boussinesq–Love equation is obtained. Based on the Riemann function, an explicit formula for the solution to the Cauchy problem is found.