Solitary Waves for Nonconvex FPU Lattices
نویسندگان
چکیده
منابع مشابه
Solitary Waves for Nonconvex FPU Lattices
Solitary waves in a one-dimensional chain of atoms {qj}j∈Z are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated the invariance of the equations allows one to transform a system with non-c...
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Small-amplitude waves in the Fermi-Pasta-Ulam (FPU) lattice with weakly anharmonic interaction potentials are described by the generalized Korteweg-de Vries (KdV) equation. Justification of the small-amplitude approximation is usually performed on the time scale, for which dynamics of the KdV equation is defined. We show how to extend justification analysis on longer time intervals provided dyn...
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Solitary waves in lattices, represented by homoclinic traveling wave trajectories of discrete dynamical systems, play a crucial role in many areas of science from condensed matter theory to biophysics [1]. In integrable systems solitary waves, known as solitons or quasiparticles, are understood rather thoroughly, with Toda lattice being the most prominent example that covers the whole range of ...
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Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schrödinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a large number of lattice periods. In this limit, the allowed positions of solitary waves relative to the lattice, as well as their linear stability properties, h...
متن کاملApproximation of Polyatomic FPU Lattices by KdV Equations
We consider the evolution of small amplitude, long wavelength initial data by a polyatomic Fermi–Pasta–Ulam lattice differential equation whose material properties vary periodically. Using the methods of homogenization theory, we prove rigorous estimates that show that the solution breaks up into the linear superposition of two appropriately scaled and modulated counterpropagating waves, each o...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Science
سال: 2006
ISSN: 0938-8974,1432-1467
DOI: 10.1007/s00332-005-0735-0