Exact Solutions of a Nonclassical Equation with a Nonlinearity under the Laplacian

Аннотация

We study a nonlinear partial differential equation that models processes occurring in a semiconductor medium. Six classes of exact solutions of this equation expressed via elementary and special functions are obtained. The qualitative behavior of these solutions is analyzed. We show that some of them are bounded and some of them “blow up” (become infinite in finite time).