Universality in the Profile of the Semiclassical Limit Solutions to the Focusing Nonlinear Schrodinger Equation at the First Breaking Curve [PDF]
International Mathematics Research Notices, 2009 40 pages, 10 ...
Alexander Tovbis +2 more
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Nonlinear Klein-Gordon equation fot nanoscale heat and mass transport [PDF]
arXiv, 2006 In this paper nonlinear Klein-Gordon equation for heat and mass transport in nanoscale was proposed and solved. It was shown that for ultra-short laser pulses nonlinear Klein-Gordon equation is reduced to nonlinear d`Alembert equation. The implicit solution of the d`Alembert equation for ultrashort laser pulses was obtained Key words: nonlinear Klein ...
arxiv
A Posteriori Error Analysis for Evolution Nonlinear Schrodinger Equations Up to the Critical Exponent [PDF]
, 2018 We provide a posteriori error estimates in the L8([0, T]; L2(?))-norm for relaxation time discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger equations up to the critical exponent.
Katsaounis, Theodoros, Kyza, Irene
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Nonlinear differential equations with exact solutions [PDF]
arXiv, 2003 New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption that nonlinear differential equations have exact solution which is general solution of the simplest integrable ...
arxiv
Approach to first-order exact solutions of the Ablowitz-Ladik equation [PDF]
, 2011 We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function.
Akhmediev, Nail +2 more
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Internal control of the Schrödinger equation [PDF]
, 2014 In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schrödinger equation.
Laurent, Camille
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Two-dimensional periodic waves in supersonic flow of a Bose–Einstein condensate [PDF]
, 2006 Stationary periodic solutions of the two-dimensional Gross–Pitaevskii equation are obtained and analysed for different parameter values in the context of the problem of a supersonic flow of a Bose–Einstein condensate past an obstacle.
El, Gennady +2 more
core +3 more sources
Simplest equation method to look for exact solutions of nonlinear differential equations [PDF]
, 2004 New method is presented to look for exact solutions of nonlinear differential equations. Two basic ideas are at the heart of our approach. One of them is to use the general solutions of the simplest nonlinear differential equations. Another idea is to take into consideration all possible singularities of equation studied. Application of our approach to
arxiv +1 more source
Nonlinear Schr��dinger Type Equations with Asymptotically Linear Terms
, 2002 We study the nonlinear Schr dinger type equation - u + ( g(x) + l)u = f(u) on the whole space R^N. The nonlinearity f is assumed to be asymptotically linear and g(x) 0 has a potential well. We do not assume a limit for g(x) as lxl . Using variational techniques, we prove the existence of a positive solution for large.
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An averaging theorem for nonlinear Schrödinger equations with small nonlinearities
Discrete & Continuous Dynamical Systems - A, 2014 Consider nonlinear Schr dinger equations with small nonlinearities \[\frac{d}{dt}u+i(-\triangle u+V(x)u)= \mathcal{P}(\triangle u,u,x),\quad x\in \mathbb{T}^d.\eqno{(*)}\] Let $\{ _1(x), _2(x),\dots\}$ be the $L_2$-basis formed by eigenfunctions of the operator $-\triangle +V(x)$.
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