Scattering of Solitons for Dirac Equation Coupled to a Particle
نویسندگان
چکیده
We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and symplectic projection onto solitary manifold in the Hilbert phase space. Supported partly by Alexander von Humboldt Research Award. Supported partly by grants of FWF, DFG and RFBR. 2
منابع مشابه
Compressive and rarefactive dust-ion acoustic solitary waves in four components quantum plasma with dust-charge variation
Based on quantum hydrodynamics theory (QHD), the propagation of nonlinear quantum dust-ion acoustic (QDIA) solitary waves in a collision-less, unmagnetized four component quantum plasma consisting of electrons, positrons, ions and stationary negatively charged dust grains with dust charge variation is investigated using reductive perturbation method. The charging current to the dust grains ca...
متن کاملScattering of Solitons for Schrödinger Equation Coupled to a Particle
We establish soliton-like asymptotics for finite energy solutions to the Schrödinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold, converges to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and the symplectic projection onto solitary manifold ...
متن کاملSolitons And Periodic Solutions To The Generalized Zakharov-Kuznetsov Benjamin-Bona-Mahoney Equation
This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this pape...
متن کاملScattering of Solitons in Derivative Nonlinear Schrödinger Model
We show that the chiral soliton model recently introduced by Aglietti et al. can be made integrable by adding an attractive potential with a fixed coefficient. The modified model is equivalent to the derivative nonlinear Schrödinger model which does not possess parity and Galilean invariance. We obtain explicit one and two classical soliton solutions and show that in the weak coupling limit, th...
متن کاملComplexition and solitary wave solutions of the (2+1)-dimensional dispersive long wave equations
In this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. The traveling wave hypothesis yields complexiton solutions. Subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. The constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...
متن کامل