Chaos and order in non-integrable model field theories

Conference · Sun Jan 01 00:00:00 EST 1989

OSTI ID:6414996

Campbell, D K; Peyrard, M

We illustrate the presence of chaos and order in non-integrable, classical field theories, which we view as many-degree-of-freedom Hamiltonian nonlinear dynamical systems. For definiteness, we focus on the {chi}{sup 4} theory and compare and contrast it with the celebrated integrable sine-Gordon equation. We introduce and investigate two specific problems: the interactions of solitary kink''-like waves in non-integrable theories; and the existence of stable breather'' solutions -- spatially-localized, time-periodic nonlinear waves -- in the {chi}{sup 4} theory. For the former problem we review the rather well developed understanding, based on a combination of computational simulations and heuristic analytic models, of the presence of a sequence of resonances in the kink-antikink interactions as a function of the relative velocity of the interaction. For the latter problem we discuss first the case of the continuum {chi}{sup 4} theory. We discuss the multiple-scale asymptotic perturbation theory arguments which first suggested the existence of {chi}{sup 4} breathers, then the subsequent discovery of terms beyond-all-orders'' in the perturbation expansion which destroy the putative breather, and finally, the recent rigorous proofs of the non-existence of breathers in the continuum theory. We then present some very recent numerical results on the existence of breathers in discrete {chi}{sup 4} theories which show an intricate interweaving of stable and unstable breather solutions on finite discrete lattices. We develop a heuristic theoretical explanation of the regions of stability and instability.

• Research Organization: Los Alamos National Lab., NM (USA)
• Sponsoring Organization: DOE/AD
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6414996
• Report Number(s): LA-UR-90-3373; CONF-8907226-1; ON: DE91002313; TRN: 91-000007
• Resource Relation: Conference: AIP chaos conference, Woodsaw, MA (USA), 24 Jul 1989
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FIELD THEORIES
RANDOMNESS
HAMILTONIANS
KLEIN-GORDON EQUATION
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
OPTICAL DISPERSION
PERTURBATION THEORY
SCATTERING
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
WAVE EQUATIONS
645400* - High Energy Physics- Field Theory
657000 - Theoretical & Mathematical Physics