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Polynomial level-set methods for nonlinear dynamical systems analysis
dynamical systems analysis level-set methods
2015/6/19
In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. Th...
Forced Nonlinear Resonance in a System of Coupled Oscillators
Forced Nonlinear Resonance System of Coupled Oscillators
2010/12/28
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t ∼ "−2 one component of ...
Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics
Pattern Formation and Solitons (nlin.PS) Quantum Gases (cond-mat.quant-gas)
2010/11/10
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solito...
Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption
Global dynamics above the ground state the nonlinear Klein-Gordon equation
2010/11/8
We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy a...
Nearly linear dynamics of nonlinear dispersive waves
Nearly linear dynamics nonlinear dispersive waves
2010/12/14
Dispersive averaging e ects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly.