# Coupled Ablowitz-Ladik equations with branched dispersion

## TL;DR

This paper investigates a multicomponent Ablowitz-Ladik system with branched dispersion, demonstrating its complete integrability and multisoliton solutions, and shows how to derive these from a simpler diagonal system via periodic reduction.

## Contribution

It introduces a multicomponent Ablowitz-Ladik system with branched dispersion and establishes its integrability and multisoliton solutions, extending previous models.

## Key findings

- Proves complete integrability of the multicomponent system
- Constructs multisoliton solutions for the system
- Shows derivation from a diagonal Ablowitz-Ladik equation via periodic reduction

## Abstract

Complete integrability and multisoliton solutions are discussed for a multicomponent Ablowitz-Ladik system with branched dispersion relation. It is also shown that starting from a "diagonal" (in two-dimensions) completely integrable Ablowitz-Ladik equation, one can obtain all the results using a periodic reduction.