The Lax integrability of a two-component hierarchy of the Burgers type dynamical systems within asymptotic and differential-algebraic approaches

TL;DR

This paper investigates the Lax integrability of a two-component Burgers-type system using differential-algebraic methods, constructs its Lax representation, and derives an integrable hierarchy with associated Lax forms.

Contribution

It introduces a novel differential-algebraic approach to establish Lax integrability and constructs a hierarchy of related integrable systems with explicit Lax representations.

Findings

Constructed the linear adjoint matrix Lax representation.

Derived a recursion operator and an infinite hierarchy of integrable systems.

Presented Lax type representations for the hierarchy.

Abstract

The Lax type integrability of a two-component polynomial Burgers type dynamical system within a differential-algebraic approach is studied, its linear adjoint matrix Lax representation is constructed. A related recursion operator and infnite hierarchy of Lax integrable nonlinear dynamical systems of the Burgers-Korteweg-de Vries type are derived by means of the gradient-holonomic technique, the corresponding Lax type representations are presented.