相关论文: Properties of some nonlinear Schrodinger equations…

I begin by reviewing the arguments leading to a nonlinear generalisation of Schrodinger's equation within the context of the maximum uncertainty principle. Some exact and perturbative properties of that equation are then summarised: those…

Using perturbative methods, we analyse a nonlinear generalisation of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of…

We consider a nonlinear semi-classical Schrodinger equation for which it is known that quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. If the initial data is an energy bounded sequence, we…

Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear…

A nonlinear generalisation of Schrodinger's equation is obtained using information-theoretic arguments. The nonlinearities are controlled by an intrinsic length scale and involve derivatives to all orders thus making the equation mildly…

A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative…

Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…

In this paper, classical small perturbations against a stationary solution of the nonlinear Schrodinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over…

Interesting nonlinear generalization of both Schr\"odinger's and Klein-Gordon's equations have been recently advanced by Tsallis, Rego-Monteiro, and Tsallis (NRT) in [Phys. Rev. Lett. {\bf 106}, 140601 (2011)]. There is much current…

A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in…

We consider the nonlinear derivative Schrodinger equation with a quintic nonlinearity, on the one dimensional torus. We exhibit that the nonlinear dynamic properties consist of four frequency modes initially excited, whose frequencies…

A chirped parametrically driven discrete nonlinear Schrodinger equation is discussed. It is shown that the system allows two resonant excitation mechanisms, i.e., successive two-level transitions (ladder climbing) or a continuous…

We study second-order electromagnetic perturbations in the Schwarzschild background and derive the effective source terms for Regge-Wheeler equation which are quadratic in first-order gravitational and electromagnetic perturbations. In…

In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schr\"odinger equation with various initial data, deterministic and random. We show that nonlinear solutions enjoy the same…

We consider the Schrodinger equation with an external potential and a cubic nonlinearity, in the semiclassical limit. The initial data are sums of WKB states, with smooth phases and smooth, compactly supported initial amplitudes, with…

It is shown that Schroedinger equation is not consistent with information theory. From the modified form of information which ensures that the most probable density function it yields tallies with a general form of continuous Riemann…

We consider a recently proposed nonlinear Schroedinger equation exhibiting soliton-like solutions of the power-law form $e_q^{i(kx-wt)}$, involving the $q$-exponential function which naturally emerges within nonextensive thermostatistics…

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…

It is shown that a large subset of initial data with finite energy ($L^2$ norm)evolves nearly linearly in nonlinear Schr\" odinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such…

Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalisation invariance and positivity. Those measures are then used to motivate generalised Lagrangians meant to probe…