A class of homogeneous nonlinear evolution equations with stable, localized solutions in any dimension

Journal Article · Mon Sep 01 00:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532144· OSTI ID:538444

Auberson, G ^[1]

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1. Laboratoire de Physique Mathematique et Theorique, UPRES-CNRS A 5032, Universite de Montpellier II, 34095 Montpellier Cedex 5 (France)

A new set of nonlinear evolution equations is introduced and studied. These equations derive from a local Lagrangian and are (i) homogeneous and (ii) invariant under the Galilei group or the Lorentz group (including time reversal). Some of them have confined solutions with a solitonlike behavior, irrespective of the space dimension. Moreover, these solutions are shown to be stable against small and localized perturbations. Another family of localized solutions is worked out, and briefly discussed with regard to the elusive integrability properties of the new equations. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 538444
• Journal Information: Journal of Mathematical Physics, Vol. 38, Issue 9; Other Information: PBD: Sep 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTUM FIELD THEORY
LAGRANGIAN FUNCTION
EQUATIONS OF MOTION
LAGRANGIAN FIELD THEORY
NONLINEAR PROBLEMS
GALILEI TRANSFORMATIONS
LORENTZ GROUPS
T INVARIANCE
SOLITONS
SCHROEDINGER EQUATION