相关论文: The Cauchy Problem for a Forced Harmonic Oscillato…

New exact and asymptotic results for a quantum inverted oscillator, driven by the variable external force, are presented. To illustrate the advantages of our approach, we applied the obtained propagator to the descriptions of evolution the…

We study the dynamics of a chain of coupled particles subjected to a restoring force (Klein-Gordon lattice) in the cases of either periodic or Dirichlet boundary conditions. Precisely, we prove that, when the initial data are of small…

We investigate scattering properties of a Moyal deformed version of the nonlinear Schr\"odinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general…

Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of…

We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator which provide, at the classical level, the same equation of motion as the conventional Hamiltonian. These Hamiltonians, say $K_{1}$ and $K_{2}$, result to be…

We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from…

We study the Cauchy problem for Schr\"odinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy…

We consider an one-dimensional inhomogeneous harmonic chain consisting of two different semi-infinite chains of harmonic oscillators. We study the Cauchy problem with random initial data. Under some restrictions on the interaction between…

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…

We solve the Cauchy problem for the Schr\"odinger equation corresponding to the family of Hamiltonians $H_{\gamma(t)}$ in $L^{2}(\mathbb{R})$ which describes a $\delta'$-interaction with time-dependent strength $1/\gamma(t)$. We prove that…

For a one-dimensional mildly quasilinear wave equation given in the upper half-plane, we consider the Cauchy problem. The initial conditions have discontinuity of the first kind at one point. We construct the solution using the method of…

We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…

The scalar wave equation in Kasner spacetime is solved, first for a particular choice of Kasner parameters, by relating the integrand in the wave packet to the Bessel functions. An alternative integral representation is also displayed,…

The inhomogenous time-fractional telegraph equation with Caputo derevatives with constant coefficients is considered. For considered equation the general representation of regular solution in rectangular domain is obtained, and the…

We point out a rather effective approach for solving the time-dependent harmonic oscillator $\ddot q=-\omega^2 q$ under various regularity assumptions. Where $\omega(t )$ is $C^1$ this is reduced to Hamilton equation for the angle variable…

We construct spectral decomposition of 1D Fokker - Planck differential operator. This reveal solution of Cauchy problem. We develop fundamental solution of Cauchy problem and compare it with one obtained by other means in our former work…

The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions…

We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive…

We consider a slowly decaying oscillatory potential such that the corresponding 1D Schr\"odinger operator has a positive eigenvalue embedded into the absolutely continuous spectrum. This potential does not fall into a known class of initial…

In this work we prove that the initial value problem (IVP) associated to the fractional two-dimensional Benjamin-Ono equation $$\left. \begin{array}{rl} u_t+D_x^{\alpha} u_x +\mathcal Hu_{yy} +uu_x &=0,\qquad\qquad (x,y)\in\mathbb R^2,\;…