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On the semi-classical limit for the focusing nonlinear Schrodinger equation: sensitivity to analytic properties of the initial data
focusing nonlinear Schrodinger equation semiclassical limit non-analyticity
2015/3/19
We present the results of a large number of careful numerical experiments carried out to investigate the way that the solution of the integrable focusing nonlinear Schrodinger equation with - xed ini...
Classification of radial solutions of the focusing, energy-critical wave equation
Classification radial solutions focusing energy-critical wave equation Analysis of PDEs
2012/4/17
In this paper, we describe the asymptotic behaviour of globally defined solutions and of bounded solutions blowing up in finite time of the radial energy-critical focusing non-linear wave equation in ...
The semiclassical limit of focusing NLS for a family of non-analytic initial data
semiclassical limit non-analytic initial data NLS
2011/7/7
The small dispersion limit of the focusing nonlinear Schro\"odinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales....
Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation
threshold for blowup one-dimensional nonlinear Klein-Gordon equation
2011/1/18
We study dynamics near the threshold for blowup in the focusing nonlinear Klein-Gordon equa-
tion utt −uxx +u−|u|2 u = 0 on the line. Using mixed numerical and analytical methods we find
...
Decay of Resonance Structure and Trapping Effect in Potential Scattering Problem of Self-Focusing Wave Packet
Quantum Gases (cond-mat.quant-gas) Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/10
Potential scattering problems governed by the time dependent Gross-Pitaevskii equation are investigated numerically for various values of coupling constants. The initial condition is assumed to have t...
Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation
the blowup/global existence dichotomy the focusing cubic nonlinear Klein-Gordon equation
2010/11/15
We present some numerical findings concerning the nature of the blowup vs. global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation in three dimensions for radial data. The co...