Hirota's Solitons in the Affine and the Conformal Affine Toda Models

TL;DR

This paper develops a recursive Hirota's method to construct comprehensive soliton solutions for affine Toda models based on any Lie algebra, introduces new soliton classes, and derives a universal mass formula, emphasizing the embedding in conformal models.

Contribution

It presents a recursive Hirota's scheme for all Lie algebra-based affine Toda solitons, including new classes, and establishes a universal mass formula through conformal embedding.

Findings

Constructed complete soliton solutions for affine Toda models.

Discovered new classes of solitons related to degeneracies.

Derived a universal mass formula applicable to all Lie groups.

Abstract

We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different type of degeneracies encountered in the Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the Affine Toda model valid for all underlying Lie groups. Embedding of the Affine Toda model in the Conformal Affine Toda model plays a crucial role in this analysis.