On a solution of a initial boundary value problem for a nonlinear equation (Q1278168)

Global existence and uniqueness theorems are proved for the equation describing the process of stationary plasma self-focusing under the natural restrictions on the smoothness of the domain boundary. During the proof, we obtain that there exists a conservation law for the norm of the strength vector for this model. Notice that, e.g., the Schrödinger equation with the cubic nonlinearity does not possess this property.