Fractal structure in the scalar. lambda. (. phi. sup 2 minus 1) sup 2 theory

Journal Article · Thu Aug 15 04:00:00 EDT 1991 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.44.1147· OSTI ID:5310212

Anninos, P; Oliveira, S; Matzner, R A ^[1]

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1. Department of Physics and Center for Relativity, The University of Texas at Austin, Austin, Texas (USA)

Head-on collisions of kink and antikink solitons are investigated numerically in the classical one-dimensional {lambda}({phi}{sup 2}{minus}1){sup 2} model. It is shown that whether a kink-antikink interaction settles to a bound state or a two-soliton solution depends fractally'' on the impact velocity. We discuss the results using the framework of perturbation theory which helps to clarify the nature of the fractal structure in terms of resonances with the internal shape mode oscillations. We also review the technique of collective coordinates used to reduce the infinite-dimensional system to one with just two degrees of freedom. Although we do not expect exact agreement by using such a simplification, we show that the reduced system bears a striking qualitative resemblance to the full infinite-dimensional system, reproducing the fractal structure. The maximum Lyapunov exponents are computed for the bound-state oscillations and found to be {similar to}0.3 for both the full and reduced systems, demonstrating the chaotic nature of the bound state.

• OSTI ID: 5310212
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 44:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUND STATE
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
DOMAIN STRUCTURE
EQUATIONS
EQUATIONS OF MOTION
FIELD EQUATIONS
FRACTALS
INSTABILITY
INTERACTIONS
KINK INSTABILITY
MECHANICS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
PERTURBATION THEORY
PHASE TRANSFORMATIONS
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
QUASI PARTICLES
SCALAR FIELDS
SINE-GORDON EQUATION
SOLITONS
UNIVERSE