Comment on `Painlev\'e Integrability and Multi-wave pattern for (2+1) dimensional Long wave-Short wave Resonance Interaction system'

TL;DR

This paper critically examines claims of integrability and solutions for a (2+1)D long wave-short wave resonance system, demonstrating it is non-integrable and highlighting inconsistencies in previous work.

Contribution

It provides a rigorous analysis showing the system's non-integrability and corrects misconceptions in prior studies regarding its solutions and properties.

Findings

The system does not pass Painlevé test, indicating non-integrability.

Previous solutions do not satisfy the original equations.

Claims of lumps and dromions are inconsistent with definitions.

Abstract

In the paper by Sivatharani et al [1], the authors make a tall claim about the integrability of a 2 component (2+1) dimensional Long wave Short wave Resonance Interaction (2C(2+1)LSRI) equation with mixed sign which was already claimed to be non integrable and hence known not to satisfy Painlev\'e [2] property which the authors show to pass Painlev\'e test. We have categorically shown how the system does not pass Painlev\'e test and hence non-integrable reinforcing the claim made by Maruno et al [2]. The authors claim to derive the solutions of 2C(2+1)LSRI equation which ironically do not satisfy the equation. To top it all, the authors claim to have generated lumps and dromions which again defy their very own definition.