8 research outputs found
Discrete instability in nonlinear lattices
The discrete multiscale analysis for boundary value problems in nonlinear
discrete systems leads to a first order discrete modulational instability above
a threshold amplitude for wave numbers beyond the zero of group velocity
dispersion. Applied to the electrical lattice [Phys. Rev. E, 51 (1995) 6127 ],
this acurately explains the experimental instability at wave numbers beyond
1.25 . The theory is also briefly discussed for sine-Gordon and Toda lattices.Comment: 1 figure, revtex, published: Phys. Rev. Lett. 83 (1999) 232
Multiscale Analysis of Discrete Nonlinear Evolution Equations
The method of multiscale analysis is constructed for dicrete systems of
evolution equations for which the problem is that of the far behavior of an
input boundary datum. Discrete slow space variables are introduced in a general
setting and the related finite differences are constructed. The method is
applied to a series of representative examples: the Toda lattice, the nonlinear
Klein-Gordon chain, the Takeno system and a discrete version of the
Benjamin-Bona-Mahoney equation. Among the resulting limit models we find a
discrete nonlinear Schroedinger equation (with reversed space-time), a 3-wave
resonant interaction system and a discrete modified Volterra model.Comment: published in J. Phys. A : Math. Gen. 32 (1999) 927-94