Intertwining relations and Darboux transformations for the wave equations

Using the intertwining operator technique we construct Darboux transformations for the wave equation with position-dependent effective mass and with linearly energy-dependent potentials. The formally adjoint generators of supersymmetry and two formally self-adjoint superpartner Hamiltonians are constructed and they close a quadratic pseudo-superalgebra. The Darboux transformations are constructed in differential and integral forms and an interrelation is established between them. The approach is applied to generation of isospectral potentials with additional or removal bound states or construction of new partner potentials without changing the spectrum, i.e. fully isospectral potentials. The method is illustrated by some concrete examples. The influence of distance between levels on the form of potentials is investigated. In particular, asymmetric double well potentials are generated.