Non-linear Schrödinger equation coming from the action of the particle's gravitational field on the quantum potential

Rosales, J.L.; Sánchez-Gómez, J. L.

doi:10.1016/0375-9601(92)90544-v

Cited by 31 publications

(14 citation statements)

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“…This equation known as the nonlinear Schrödinger equation (NLS), which, depending on the physical situation takes several different forms, in a general quantum system is written as i ∂ (r, t) ∂t =Ĥ (r, t), (1.1) where i = √ −1, is the wave function, is the reduced Plank's constant, andĤ is the Hamiltonian operator. Applications of the NLS equation were found in semiconductor electronics [2,3], optics in nonlinear media [4], photonics [5], plasmas [6], fundamentation of quantum mechanics [7], dynamics of accelerators [8], mean-field theory of Bose-Einstein condensates [9], or in biomolecule dynamics [10]. In some of these fields and in many others, the NLS equation appears as an asymptotic limit for a slowly varying dispersive wave envelope propagating in a nonlinear medium [11].…”

Section: Introductionmentioning

confidence: 99%

A modified numerical scheme for the cubic Schrödinger equation

Bratsos

2009

Numer. Methods Partial Differential Eq.

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A numerical scheme based on the use of rational approximants in a two-time level recurrence relation is applied to the cubic Schrödinger equation. The resulting nonlinear finite-difference scheme, which is analyzed for stability, is solved using an already known modified predictor-corrector (MPC) scheme. The efficiency of the proposed method is tested to the single and the double-soliton waves and the results arising from the experiments are compared with the relevant ones known in the available bibliography.

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Section: Introductionmentioning

confidence: 99%

A modified numerical scheme for the cubic Schrödinger equation

Bratsos

2009

Numer. Methods Partial Differential Eq.

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“…The functions β (z), γ(z), g(z), and χ(z) are, respectively, the group velocity dispersion (GVD), self-phase modulation (SPM), linear and nonlinear gain (loss). NLSE appears in many branches of physics and applied mathematics [1], such as, for example, in semiconductor electronics [2,3], optics in nonlinear media [4], photonics [5], plasmas [6], fundament of quantum mechanics [7], dynamics of accelerators [8], mean-field theory of Bose-Einstein condensates [9] or in biomolecule dynamics [10]. During the past several years, many theoretical issues concerning the NLSE have received considerable attention.…”

Section: Introductionmentioning

confidence: 99%

Chirped Wave Solutions of a Generalized (3+1)-Dimensional Nonlinear Schr¨odinger Equation

Lai

Cai

2011

Zeitschrift Für Naturforschung A

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The exact chirped soliton-like and quasi-periodic wave solutions of the (3+1)-dimensional generalized nonlinear Schrödinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in this paper. The form and the behaviour of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain (loss).

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“…Nonlinear Schrödinger (NLS) equations appear in a great array of contexts [1], for example in semiconductor electronics [2,3], optics in nonlinear media [4], photonics [5], plasmas [6], the fundamentation of quantum mechanics [7], the dynamics of accelerators [8], the mean-field theory of Bose-Einstein condensates [9] or in biomolecule dynamics [10]. In some of these fields and in many others, the NLS equation appears as an asymptotic limit for a slowly varying dispersive wave envelope propagating a nonlinear medium [11].…”

Section: Introductionmentioning

confidence: 99%