ON SCHRODINGER-EQUATIONS WITH CONCENTRATED NONLINEARITIES

Schrodinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have inte resting mathematical properties. We show that in the semiclassical lim it it is possible to separate the relevant degrees of freedom by notin g that in the regions where the nonlinearities are effective all state s are suppressed but the metastable ones (resonances). In this way the description of the nonlinear regions is reduced to ordinary different ial equations weakly coupled to standard Schrodinger equations valid i n the linear regions. The idea is illustrated through the study of a p rototype equation recently proposed for resonant tunneling of electron s through a double barrier heterostructure and for which nonlinear osc illations have been numerically predicted. (C) 1995 Academic Press, In c.