Novel nonlinear wave equation: regulated rogue waves and accelerated soliton solutions

TL;DR

This paper introduces a new exactly solvable complex nonlinear wave equation that models rogue waves with controllable features and includes novel accelerated dark soliton solutions, expanding understanding of wave dynamics.

Contribution

The paper presents a novel (1+1)-dimensional complex nonlinear wave equation with exact solutions for rogue waves and accelerated dark solitons, offering new insights into wave regulation and topology change.

Findings

Discovery of a rogue wave with adjustable amplitude and width.

Existence of accelerated dark soliton solutions despite constant coefficients.

Rich analytic properties of the new wave equation.

Abstract

A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation.