We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The heat kernel is given in terms ofâ€¦ (More)

We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent SchrÃ¶dinger equation with variableâ€¦ (More)

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent SchrÃ¶dinger equation with variable quadraticâ€¦ (More)

We study multi-parameter solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation which include oscillating laser beams in a parabolic waveguide, spiral lightâ€¦ (More)

We discuss an integral form of the Cauchy initial value problem for the nonlinear SchrÃ¶dinger equation with variable coefficients. Some special and limiting cases are outlined.

In this paper, by means of similarity transformations we study exact analytical solutions for a generalized nonlinear Schr Ìˆo dinger equation with variable coefficients. This equation appears inâ€¦ (More)

We discuss a method of constructing solutions of the initial value problem for diffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-typeâ€¦ (More)

Explicit solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation are applied to wave fields with invariant features, such as oscillating laser beams in aâ€¦ (More)

We construct an explicit solution of the Cauchy initial value problem for the timedependent SchrÃ¶dinger equation for a charged particle with a spin moving in a uniform magnetic field and aâ€¦ (More)