Explicit lump and line rogue wave solutions to a modified Hietarinta equation

TL;DR

This paper derives explicit lump and rogue wave solutions for a new 2+1 dimensional nonlinear equation, analyzing their behavior and properties using computational tools and graphical visualizations.

Contribution

It introduces novel lump and rogue wave solutions for a specific nonlinear equation, expanding the understanding of such solutions in higher dimensions.

Findings

Lump solutions are spatially localized and can transform into rogue waves under certain parameters.

Graphical analysis reveals the dynamical behavior and interaction patterns of the solutions.

The study demonstrates the applicability of computer algebra systems in deriving and analyzing complex wave solutions.

Abstract

Lump solutions are spatially rationally localized solutions which usually arise as solutions to higher dimensional nonlinear partial differential equations often possessing Hirota bilinear forms. Under some parameter constraint, these solutions may lead to rogue wave solutions. In this article, we study lump and rogue wave solutions of a new nonlinear non-evolutionary equation in 2+1 dimensions with the aid of a computer algebra system. We present illustrative examples and analyze the dynamical behavior of the solutions using graphical representations