scholarly journals Solitons for the Nonlinear Klein-Gordon Equation

2010 ◽  
Vol 10 (2) ◽  
Author(s):  
J. Bellazzini ◽  
V. Benci ◽  
C. Bonanno ◽  
A.M. Micheletti
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Energy Charge ◽  
Sufficient Conditions ◽  
Orbital Stability ◽  
Field Equations ◽  
Klein Gordon ◽  
Ratio Energy ◽  
Klein Gordon Equation

AbstractIn this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a function, which turns out to be a useful approach for many field equations.

scholarly journals Multi-Solitary Waves for the Nonlinear Klein-Gordon Equation

2014 ◽  
Vol 39 (8) ◽  
pp. 1479-1522 ◽  
Author(s):  
Jacopo Bellazzini ◽  
Marco Ghimenti ◽  
Stefan Le Coz
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS

2002 ◽  
Vol 14 (04) ◽  
pp. 409-420 ◽  
Author(s):  
VIERI BENCI ◽  
DONATO FORTUNATO FORTUNATO
Keyword(s):  
Electromagnetic Field ◽  
Solitary Wave ◽  
Electric Field ◽  
Solitary Waves ◽  
Maxwell Equations ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.

On the Orbital Stability of Standing-Wave Solutions to a Coupled Non-Linear Klein-Gordon Equation

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Daniele Garrisi
Keyword(s):  
Standing Wave ◽  
Ground State ◽  
Gordon Equation ◽  
Standing Waves ◽  
Orbital Stability ◽  
Wave Solutions ◽  
Non Linear ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractWe show the existence of standing-wave solutions to a coupled non-linear Klein-Gordon equation. Our solutions are obtained as minimizers of the energy under a two-charges constraint. We prove that the ground state is stable and that standing-waves are orbitally stable under a non-degeneracy assumption.

AC Driven Directed Motion of Solitary Waves

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4428-4433 ◽  
Author(s):  
Yaroslav Zolotaryuk ◽  
Peter L. Christiansen ◽  
Mario Salerno
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Directed Motion ◽  
Temporal Asymmetry ◽  
Topological Soliton ◽  
System Parameters ◽  
Broken Symmetries ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Unidirectional Motion

We study the possibility of unidirectional motion of a topological soliton of a dissipative (continuous and discrete) Klein-Gordon equation driven by AC forces with certain broken symmetries and with zero mean. The role played by the temporal asymmetry of the system in establishing soliton DC motions which resemble usual soliton ratchets is emphasized. The dependence of the soliton velocity on the system parameters is studied.

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