ﻻ يوجد ملخص باللغة العربية
We show that a nonlinear Schrodinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schrodinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantum-like features appear and is equivalent to scaling Plancks constant.
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of problems. An ex
We study the time-asymptotic behavior of solutions of the Schrodinger equation with nonlinear dissipation begin{equation*} partial _t u = i Delta u + lambda |u|^alpha u end{equation*} in ${mathbb R}^N $, $Ngeq1$, where $lambdain {mathbb C}$, $Re la
We consider the Schrodinger equation with nonlinear dissipation begin{equation*} i partial _t u +Delta u=lambda|u|^{alpha}u end{equation*} in ${mathbb R}^N $, $Ngeq1$, where $lambdain {mathbb C} $ with $Imlambda<0$. Assuming $frac {2} {N+2}<alpha<fra
We perform a numerical study of the initial-boundary value problem, with vanishing boundary conditions, of a driven nonlinear Schrodinger equation (NLS) with linear damping and a Gaussian driver. We identify Peregrine-like rogue waveforms, excited by
Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic func