In this article, nonlinear propagation of envelope gravity waves is studied in baroclinic atmosphere. The classical (2 + 1) dimensional nonlinear Schrödinger (NLS) equation can be derived by using the multiple-scale, perturbation method. Further, via the semi-inverse method, the Euler–Lagrange equation and Agrawal’s method, the time–space fractional (2 + 1) dimensional nonlinear Schrödinger (FN...

Solutions to a singular one-dimensional Vlasov equation are obtained as the semiclassical limit of the Wigner transform associated to a logarithmic Schrödinger equation. Two frameworks are considered, regarding in particular the initial position density: Gaussian initial density, or smooth initial density away from vacuum. For Gaussian initial densities, the analysis also yields global solution...

A static scission configuration in cold ternary fission has been considered in the framework of two mean field approaches. The virial theorems has been suggested to investigate correlations in the phase space, starting from a kinetic equation. The inverse mean field method is applied to solve single-particle Schrödinger equation, instead of constrained selfconsistent Hartree–Fock equations. It ...

In this paper we consider the Moutard transformation [9] which is a twodimensional version of the well-known Darboux transformation. We give an algebraic interpretation of the Moutard transformation as a conjugation in an appropriate ring and the corresponding version of the algebro-geometric formalism for two-dimensional Schrödinger operators. An application to some problems of the spectral th...

We propose a new approach for the study of the time evolution of a factorized N -particle bosonic wave function with respect to a mean-field dynamics with a bounded interaction potential. The new technique, which is based on the control of the growth of the correlations among the particles, leads to quantitative bounds on the difference between the many-particle Schrödinger dynamics and the one...

We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potent...

The study of time-periodic solutions the multidimensional wave equation on entire 3D space is an important field research in applied mathematics. It known that this leads to Sommerfeld radiation condition at infinity. states for a solution one-dimensional equation, such as Helmholtz or represent outgoing 1D, which models propagation electromagnetic waves systems effectively reduced one dimensio...

This paper develops a spectral expansion approach to the valuation of contingent claims when the underlying state variable follows a one-dimensional diffusion with the infinitesimal variance a(x), drift b(x) and instantaneous discount (killing) rate r(x). The Spectral Theorem for self-adjoint operators in Hilbert space yields the spectral decomposition of the contingent claim value function. Ba...