Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

TL;DR

This paper introduces a differential-algebraic method to analyze the integrability of generalized Riemann and Korteweg-de Vries hydrodynamical equations, providing new insights into their Lax type integrability.

Contribution

It develops a novel differential-algebraic approach for studying Lax type integrability of complex hydrodynamical equations, extending analysis to generalized Riemann and KdV systems.

Findings

Established Lax type integrability for generalized Riemann equations at N=3,4

Applied the approach successfully to Korteweg-de Vries system

Provided a framework for analyzing integrability of hydrodynamical equations

Abstract

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.