Riemann problems in FPU chains
نویسندگان
چکیده
منابع مشابه
Riemann solvers and undercompressive shocks of convex FPU chains
We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space-time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We all...
متن کاملSymmetry and resonance in periodic FPU chains
The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This ‘Birkhoff-Gustavson normal form’ retains the symmetries of the original system and we show that in most cases this allows us to view the periodic FPU Hamiltonian as a...
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In this paper we prove that near the equilibirum position any periodic FPU chain with an odd number of particles admits a Birkhoff normal form up to order 4, and we obtain an explicit formula of the Hessian of its Hamiltonian at the fixed point.
متن کاملUnimodal wave trains and solitons in convex FPU chains
We consider atomic chains with nearest neighbour interactions and study periodic and homoclinic travelling waves which are called wave trains and solitons, respectively. Our main result is a new existence proof which relies on the constrained maximisation of the potential energy and exploits the invariance properties of an improvement operator. The approach is restricted to convex interaction p...
متن کاملHeteroclinic Travelling Waves in Convex FPU-Type Chains
We consider infinite FPU-type atomic chains with general convex potentials and study the existence of monotone fronts that are heteroclinic travelling waves connecting constant asymptotic states. Iooss showed that small amplitude fronts bifurcate from convex-concave turning points of the force. In this paper we prove that fronts exist for any asymptotic states that satisfy a certain algebraic c...
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ژورنال
عنوان ژورنال: PAMM
سال: 2007
ISSN: 1617-7061,1617-7061
DOI: 10.1002/pamm.200700786