Narrow Results

The exact solutions of Wick-type stochastic nonlinear Schrödinger equation (NLSE) using extended auxiliary equation method (EAEM) has been obtained in this paper. Hermite transform has been used for transforming the stochastic NLSE into deterministic PDE. Also, the stochastic solutions in the white noise space have been obtained by applying inverse Hermite transform on the deterministic set of solutions.

In this paper we study the Cauchy problem for the wave equation with spacetime Lévy noise initial data in the Kondratiev space of stochastic distributions. We prove that this problem has a strong and unique C²-solution, which takes an explicit form. Our approach is based on the use of the Hermite transform.