On the Inverse Scattering Problem for the Schrodinger Equation with Increasing Potential

The one-dimensional Schrdinger equation on the entire axis is considered, the potential of which at the left end grows as a quadratic function, and at the right end as a linear function.The inverse scattering problem is studied by the method of transformation operators.The main integral equations of the Marchenko type are obtained, allowing the inverse problem to be solved.