20 citations · 59 across the 11 of their papers we have counts for
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Newton's law for a trajectory of concentration of solutions to nonlinear Schrodinger equation
Anatoli Babin, Alexander Figotin
One of important problems in mathematical physics concerns derivation of point dynamics from field equations. The most common approach to this problem is based on WKB method. Here…
On the regularization mechanism for the periodic Korteweg-de Vries equation
Anatoli V. Babin, Alexei A. Ilyin, Edriss S. Titi
In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg--de Vries (KdV) equation in the homogeneous S…
Nonlinear dynamics of a system of particle-like wavepackets
A. Babin, A. Figotin
This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coef…
Wavepacket preservation under nonlinear evolution
A. Babin, A. Figotin
We study nonlinear systems of hyperbolic (in a wider sense) PDE's in entire d-dimensional space describing wave propagation with the initial data in the form of a finite sum of wav…
Linear superposition in nonlinear wave dynamics
A. Babin, A. Figotin
We study nonlinear dispersive wave systems described by hyperbolic PDE's in R^{d} and difference equations on the lattice Z^{d}. The systems involve two small parameters: one is th…