General bright and dark soliton solutions to the massive Thirring model via KP hierarchy reductions

TL;DR

This paper derives general bright and dark soliton solutions for the massive Thirring model using KP hierarchy reductions, providing explicit solutions and analyzing their properties under various boundary conditions.

Contribution

It introduces a novel method to obtain both bright and dark soliton solutions for the massive Thirring model via KP hierarchy reductions and tau function techniques.

Findings

Explicit multi-bright soliton solutions derived

General dark soliton solutions constructed from discrete KP tau functions

Detailed analysis of one- and two-soliton dynamics and properties

Abstract

In the present paper, we are concerned with the tau function and its connection with the Kadomtsev-Petviashvili (KP) theory for the massive Thirring (MT) model. First, we bilinearize the massive Thirring model under both the vanishing and nonvanishing boundary conditions. Starting from a set of bilinear equations of two-component KP-Toda hierarchy, we derive the multi-bright solution to the MT model by the KP hierarchy reductions. Then, we show that the discrete KP equation can generate a set of bilinear equations of a deformed KP-Toda hierarchy through Miwa transformation. By imposing constraints on the parameters of the tau function, the general dark soliton solution to the MT model is constructed from the tau function of the discrete KP equation. Finally, the dynamics and properties of one- and two-soliton for both the bright and dark cases are analyzed in details.