Soliton dynamics in the ABS nonlinear spinor model with external fields
arXiv:2601.13783 · doi:10.1088/1751-8121/ac190b
Abstract
We consider the novel nonlinear model in (1 + 1)-dimensions for Dirac spinors recently introduced by Alexeeva, Barashenkov, and Saxena [1] (ABS model), which admits an exact explicit solitary-wave (soliton for short) solution. The charge, the momentum, and the energy of this solution are conserved. We investigate the dynamics of the soliton subjected to several potentials: a ramp, a harmonic, and a periodic potential. We develop a Collective Coordinates Theory by making an ansatz for a moving soliton where the position, rapidity, and momentum, are functions of time. We insert the ansatz into the Lagrangian density of the model, integrate over space and obtain a Lagrangian as a function of the collective coordinates. This Lagrangian differs only in the charge and mass with the Lagrangian of a collective coordinates theory for the Gross-Neveu equation. Thus the soliton dynamics in the ABS spinor model is qualitatively the same as in the Gross-Neveu equation, but quantitatively it differs. These results of the collective coordinates theory are confirmed by simulations, i.e., by numerical solutions for solitons of the ABS spinor model, subjected to the above potentials.
References in corpus (10)
- Soliton ratchets induced by ac forces with harmonic mixing
- Orbital stability of Dirac solitons
- Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity
- Nonlinear Dirac equation solitary waves in external fields
- Dynamics of Dirac solitons in networks
- On the nonlinear Dirac equation on noncompact metric graphs
- Forced Nonlinear Schroedinger Equation with Arbitrary Nonlinearity
- Spinor solitons and their -symmetric offspring
- Solitary waves of a PT-symmetric Nonlinear Dirac equation
- Stability of new exact solutions of the nonlinear Schrodinger equation in a Poschl-Teller external potential