Construction of Nth-order rogue wave solutions for Hirota equation by means of bilinear method

TL;DR

This paper develops a method to construct Nth-order rogue wave solutions for the Hirota equation using bilinear techniques, with solutions expressed as determinants and analysis of their dynamic patterns.

Contribution

It introduces a determinant-based bilinear method for constructing higher-order rogue wave solutions of the Hirota equation, revealing their dynamic behaviors.

Findings

Explicit Nth-order rogue wave solutions expressed as determinants

Identification of interesting dynamic patterns of rogue waves

Method applicable to integrable equations with similar structures

Abstract

In this work, we focus on the construction of Nth-rouge wave solutions for the Hirota equation by utilizing the bilinear method. The formula can be represented in terms of determinants. In addition, some interesting dynamic patterns of rogue waves are exhibited.