Relativistic dissipatons in integrable nonlinear Majorana type spinor model

TL;DR

This paper introduces a new integrable relativistic nonlinear model for Majorana spinor fields, establishes its gauge equivalence with a known spin model, constructs a dissipaton solution, and analyzes its scattering properties.

Contribution

It presents a novel integrable model for Majorana spinors, constructs explicit dissipaton solutions, and explores their resonant scattering behavior, linking it to hyperbolic complex and Thirring models.

Findings

Constructed a dissipaton solution using Hirota bilinear method.

Calculated first integrals of motion showing nonlinear relativistic particle behavior.

Identified resonant scattering properties of dissipatons.

Abstract

By method of moving frame, the relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions is introduced and gauge equivalence of this model with Papanicolau spin model on one sheet hyperboloid is established. In terms of the so called double numbers, the model is represented also as hyperbolic complex relativistic model, in the form similar to the massive Thirring model. By using Hirota bilinear method, one dissipaton solution of this model is constructed. We calculated first integrals of motion for this dissipaton and show that it represents relativistic particle with highly nonlinear mass. Analyzing resonance conditions for scattering of two relativistic dissipatons, we find a solution describing resonant property of the dissipatons.