Year: 2026
Type: article
Abstract: We obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form $ \psi(x,t) =\psi(x) \rm e^{-\rm i \omega t}$ where the nonlinear interactions are a combination of vector-vector (VV) and scalar-scalar (SS) interactions with the interaction Lagrangian given by $L_I = \frac{g^2}{(\kappa+1)}[\bar{\psi} \gamma_{\mu}\psi \bar{\psi} \gamma^{\mu} \psi]^{(\kappa+1)/2} - \frac{g^2}{q(\kappa+1)} (\bar{\psi} \psi)^{\kappa+1}$. This is the complement of the generalization of the Alexeeva, Barashenkov, Saxena (ABS) model \cite{abs} that we recently studied \cite{ak} and called the generalized ABS (i.e. gABS) model. We find that in the complementary gABS model the energy of the solitary wave divided by its charge is {\it independent} of the coupling constant $g$ in accordance to what we found in the gABS model. However, unlike the solitary wave behavior in the gABS model, in this complementary gABS model all the solitary waves have a single hump, any value of $0 < \omega < m$ is allowed and furthermore, the solitary wave bound states exist only in case $\kappa \le \kappa_c$, where $\kappa_c$ depends on the value of $q$. Here $\omega$ and $m$ denote frequency and mass respectively. We discuss the non-relativistic reduction of this complementary gABS model to a modified nonlinear Schr"odinger equation (NLSE) and discuss the stability of the solitary waves in the domain of validity of the modified NLSE.
Source: Physica Scripta
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,400
OpenAlex ID: W4415112217
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