We prove that for the L-critical nonlinear Schrödinger equations, the wave operators and their inverse are related explicitly in terms of the Fourier transform. We discuss some consequences of this property. In the onedimensional case, we show a precise similarity between the L-critical nonlinear Schrödinger equation and a nonlinear Schrödinger equation of derivative type.

This paper derives from the proceedings of an invited talk I presented at the American Conference on Theoretical Chemistry (ACTC) in 1978. Besides being timely scientifically, the paper’s creation offers some amusing insight into how science is done. Quantum chemistry approxim:’ I /so!sc4.? Schrodinger equation. To be predictive “electron correlation” must be included. In the 19505 two developm...

We present a novel formulation based on quantum Monte Carlo techniques for the treatment of volume polarization due to quantum mechanical penetration of the solute charge density in the solvent domain. The method allows to accurately solve Poisson's equation of the solvation model coupled with the Schrodinger equation for the solute. We demonstrate the performance of the approach on a represent...

Numerical studies of beam filamentation in laser-produced plasma are presented. This involves the numerical solution of the parabolic wave equation. known as the Schrodinger equation, coupled with the thermal transport equations for both ions and electrons, in two dimensions. The solutionof the resultingequationwith non-linear refractive index due to thermal and pondermotive forces. shows self-...

Minimal length in non-commutative space of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions momentum space. The eigensolutions are found system mapping to well-known Schrodinger equation Pöschl-Teller potential.

Based on computerized symbolic computation and a new general ansatz,an extended Riccati equation rational expansion method is presented to construct multiple exact solutions for nonlinear evolution equations and implemented in a computer algebraic system.The validity and reliability of the method are tested by its application to four nonlinear evolution equations arising in physics,namely,gener...

We consider two types of strongly localized modes in discrete nonlinear lattices. Taking the lattice nonlinear Schrodinger (NLS) equation as a particular but rather fundamental example, we show that (1) the discreteness effects may be understood in the "standard" discrete NLS model as arising from an effective periodic potential similar to the Peierls-Nabarro (PN) barrier potential for kinks in...

We study the conditions for soliton-like wave propagation in the Photorefractive (PR) and electro-optic (i.e., Pockels) material, by using Nonlinear Schrodinger (NLS) equation. The complete NLS equation is solved analytically and numerically by transforming it into the phase space. Our results clearly show the existence of both the dark and bright solitary solutions for the PR medium. Interesti...

The scenarios of achieving effective ionospheric modification are summarized and the likely physical processes engaging linear and nonlinear mode conversions through plasma inhomogeneity and nonlinearity are revealed. Parametric instabilities, which are the directly relevant processes to achieve effective heating of the ionospheric F region, are formulated and analyzed. The threshold fields and...

The standard quantum discrete nonlinear Schrodinger equation with periodic boundary conditions and an arbitrary number of freedoms (f) is solved exactly at the second and third quantum levels. I f f -+ x at a sufficiently small level of anharmonicity c j ) , the value for soliton binding energy from quantum field‘theory (QFT) in the continuum limit is recovered. For fixed however, the QFT resul...