Burgers and KP hierarchies: A functional representation approach

Abstract

From a 'discrete' functional zero curvature equation, functional representations of (matrix) Burgers and potential KP (pKP) hierarchies (and others), as well as corresponding Backlund transformations, can be obtained in a surprisingly simple way. With their help we show that any solution of a Burgers hierarchy is also a solution of the pKP hierarchy. Moreover, the pKP hierarchy can be expressed in the form of an inhomogeneous Burgers hierarchy. In particular, this leads to an extension of the Cole-Hopf transformation to the pKP hierarchy. Furthermore, these hierarchies are solved by the solutions of certain functional Riccati equations.

16 pages

References in corpus (3)

• Functional representations of integrable hierarchies
• From AKNS to derivative NLS hierarchies via deformations of associative products
• From nonassociativity to solutions of the KP hierarchy

Cited by in corpus (8)

• With a Cole-Hopf transformation to solutions of the noncommutative KP hierarchy in terms of Wronski matrices
• BKP and CKP revisited: The odd KP system
• A new approach to deformation equations of noncommutative KP hierarchies
• Bidifferential graded algebras and integrable systems
• Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
• Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System
• Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems
• The soliton nature of the super-Klein tunneling effect