相关论文: Exact Propagators for Soliton Potentials

In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…

By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…

We propose a procedure based on phase equivalent chains of Darboux transformations to generate local potentials satisfying the radial Schr\"odinger equation and sharing the same scattering data. For potentials related by a chain of…

In a previous paper by the second author, we discussed a characterization of the microlocal singularities for solutions to Schr\"odinger equations with long range type perturbations, using solutions to a Hamilton-Jacobi equation. In this…

By using similarity transformations approach, the exact propagator for a generalized one-dimensional Fokker-Planck equation, with linear drift force and space-time dependent diffusion coefficient, is obtained. The method is simple and…

We consider Schr\"odinger equations with variable coefficients, and it is supposed to be a long-range type perturbation of the flat Laplacian on $R^n$. We characterize the wave front set of solutions to Schr\"odinger equations in terms of…

Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…

We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded…

We prove the dispersive and Strichartz estimates for solutions to the wave equation with a class of many-electric potentials in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the…

Irreducible second-order Darboux transformations are applied to the periodic Schrodinger's operators. It is shown that for the pairs of factorization energies inside of the same forbidden band they can create new non-singular potentials…

This paper blends two techniques recently developed in [2] and [3] to prove the presence of absolutely continuous spectrum for the multidimensional Schrodinger operator provided that the potential is summable over trajectory with positive…

Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we…

Potentials of the nonstationary Schr\"{o}dinger operator constructed by means of $n$ recursive B\"{a}cklund transformations are studied in detail. Corresponding Darboux transformations of the Jost solutions are introduced. We show that…

We construct Darboux-Moutard type transforms for the two-dimensional conductivity equation. This result continues our recent studies of Darboux-Moutard type transforms for generalized analytic functions. In addition, at least, some of the…

A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schr\"odinger matrix Hamiltonians is…

We prove that the Schr\"odinger equation for N number of particles in the time dependent electro-magnetic field generates a unique unitary propagator on the state space under the condition that the field is smooth and moderately but almost…

A review of a recent method is presented to construct certain exact solutions to the focusing nonlinear Schr\"odinger equation on the line with a cubic nonlinearity. With motivation by the inverse scattering transform and help from the…

In this paper, we introduce a new notion named as Schr\"odinger soliton. So-called Schr\"odinger solitons are defined as a class of special solutions to the Schr\"odinger flow equation from a Riemannian manifold or a Lorentzian manifold $M$…

Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…

In this paper we consider an initial/boundary value problem for the Schr\"odinger equation with a right-hand side involving the fractional Sturm-Liouville operator with singular propagation and potential. To construct a solution, first…