Book Review: Discrete and continuous nonlinear Schrödinger systems
نویسندگان
چکیده
منابع مشابه
Continuous and discrete Schrödinger systems with parity-time-symmetric nonlinearities.
We investigate the dynamical behavior of continuous and discrete Schrödinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrödinger counterparts. In particular, the PT-symmetric nonlinear Schrödinger equation can simultaneously support both bright and dark soliton solutions. In additi...
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1. Nonlinear Schrödinger equation: setup and applications The nonlinear Schrödinger (NLS) equation [1, 2, 3] is a prototypical dispersive nonlinear partial differential equation (PDE) that has been central for almost four decades now to a variety of areas in Mathematical Physics. It is an equation for a complex field u(x, t) of the form: iu t = −∆u + σ|u| 2 u. u is the complex field whose spati...
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In this paper, we are concerned with the following fractional Schrödinger-Poisson system: (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...
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We present a new discrete Adomian decomposition method to approximate the theoretical solution of discrete nonlinear Schrödinger equations. The method is examined for plane waves and for single soliton waves in case of continuous, semi– discrete and fully discrete Schrödinger equations. Several illustrative examples and Mathematica program codes are presented.
متن کاملBreathers for the Discrete Nonlinear Schrödinger Equation with Nonlinear Hopping
We discuss the existence of breathers and lower bounds on their power, in nonlinear Schrödinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed-point arguments, deriving lower bounds for the power which can serve as a threshold for the existence of breather solutions. Qualitatively, the theoretical results justify non-existence of breathers below ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2005
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-05-01074-8