Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Wayne, C E"'
Autor:
Hoffman, A., Wayne, C. E.
The Backlund Transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite dimensional dynamical systems. It has recently been used to study the stabilit
Externí odkaz:
http://arxiv.org/abs/1211.2836
We prove that multi-soliton solutions of the Toda lattice are both linearly and nonlinearly stable. Our proof uses neither the inverse spectral method nor the Lax pair of the model but instead studies the linearization of the B\"acklund} transformati
Externí odkaz:
http://arxiv.org/abs/1010.5775
Autor:
Hoffman, A., Wayne, C. E.
By combining results of Mizumachi on the stability of solitons for the Toda lattice with a simple rescaling and a careful control of the KdV limit we give a simple proof that small amplitude, long-wavelength solitary waves in the Fermi-Pasta-Ulam (FP
Externí odkaz:
http://arxiv.org/abs/0811.2406
Autor:
Hoffman, A., Wayne, C. E.
We prove the existence of asymptotic two-soliton states in the Fermi-Pasta-Ulam model with general interaction potential. That is, we exhibit solutions whose difference in $\ell^2$ from the linear superposition of two solitary waves goes to zero as t
Externí odkaz:
http://arxiv.org/abs/0809.3231
Autor:
Hoffman, A., Wayne, C. E.
We study the interaction of small amplitude, long wavelength solitary waves in the Fermi-Pasta-Ulam model with general nearest-neighbor interaction potential. We establish global-in-time existence and stability of counter-propagating solitary wave so
Externí odkaz:
http://arxiv.org/abs/0806.1637
The long-time behaviour of solutions of systems of conservation laws has been extensively studied. In particular, Liu and Zeng \cite{liu:1997} have given a detailed exposition of the leading order asymptotics of solutions close to a constant backgrou
Externí odkaz:
http://arxiv.org/abs/math/0703273
Autor:
Gallay, Th., Wayne, C. E.
Burgers vortices are stationary solutions of the three-dimensional Navier-Stokes equations in the presence of a background straining flow. These solutions are given by explicit formulas only when the strain is axisymmetric. In this paper we consider
Externí odkaz:
http://arxiv.org/abs/math/0503353
Autor:
Gallay, Th., Wayne, C. E.
In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation
Externí odkaz:
http://arxiv.org/abs/math/0503354
We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium at the left
Externí odkaz:
http://arxiv.org/abs/nlin/0408020
Autor:
Gallay, Th., Wayne, C. E.
We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R^2 and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing results on the a
Externí odkaz:
http://arxiv.org/abs/math/0102197