Exact Solutions of a Second-Order Nonlinear Partial Differential Equation

Abstract

The equation ∂²u/∂t∂x + u^p∂u/∂x = u^q describing a nonstationary process in semiconductors, with parameters p and q that are a nonnegative integer and a positive integer, respectively, and satisfy p + q ≥ 2, is considered in the half-plane (x, t) ∈ ℝ × (0,∞). All in all, fourteen families of its exact solutions are constructed for various parameter values, and qualitative properties of these solutions are noted. One of these families is defined for all parameter values indicated above.