A study of two new generalized negative KdV type equations

TL;DR

This paper explores geometric interpretations of negative KdV equations, introduces higher-order variants, and demonstrates their soliton solutions through Painleve and symmetry analyses.

Contribution

It provides a novel geometric framework for higher-order negative KdV equations and analyzes their integrability and soliton solutions.

Findings

Higher-order negative KdV equations are geometrically interpreted.

Painleve analysis shows these equations are integrable.

Soliton solutions are obtained for the new equations.

Abstract

We give a simple geometric interpretation of the mapping of the negative KdV equation as proposed by Qiao and Li {arXiv:1101.1605 [math-ph], Europhys. Lett.,94 (2011) 50003} and the Fuchssteiner equation using geometry of projective connection on S1 or stabilizer set of the Virasoro orbit. We propose a similar connection between with the higher-order negative KdV equations of Fuchssteiner type described as and respectively. We study the Painleve and symmetry analyses of these newly found equations and show that they yield soliton solutions.