A coupled Volterra system and its exact solutions

TL;DR

This paper introduces a coupled Volterra system, demonstrating its integrability and deriving various exact solutions such as cnoidal waves, positons, negatons, and complexitons using a rational expansion method.

Contribution

It presents a new coupled Volterra system as an integrable discrete analogue of the coupled KdV system and provides explicit solutions using a straightforward method.

Findings

The coupled Volterra system is shown to be integrable.

Explicit solutions including cnoidal waves, positons, negatons, and complexitons are obtained.

The method simplifies finding exact solutions for discrete integrable systems.

Abstract

A coupled Volterra system is proposed. The model can be considered as one of the integrable discrete form of the coupled integrable KdV system which is a significant physical model. Many types of cnoidal waves, positons, negatons (solitons) and complexitons of the model are obtained by a simple rational expansion method of the Jacobi elliptic functions, trigonometric functions and hyperbolic functions.