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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...
By using the theory of dynamical systems, solitary and periodic wave solutions for a coupled quadratic nonlinear system are studied.
Abstract: The Hasegawa-Wakatani models are used in the study of confinement of hot plasmas with externally imposed magnetic fields. The nonlinear terms in the Hasegawa-Wakatani models complicate the a...
As a model of coupled nano-electromechanical resonantors we study two nonlinear driven oscillators with an arbitrary coupling strength between them. Analytical expressions are derived for the oscillat...
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain less well understood in terms of fundamental fluid dynamics.
We study nonlinear wave phenomena in a coupled ring resonator optical waveguide in the tight coupling regime. The discrete nonlinear Bloch modes of the structure are derived. The switching behavior of...
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 ...
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...
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...
Dispersive averaging e ects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly.
We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order...
We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress...
We consider Navier-Stokes equations coupled to nonlinear FokkerPlanck equations describing the probability distribution of particles interacting with fluids. We describe relations determining the coef...

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