On integrable structures for a generalized Monge-Ampere equation

TL;DR

This paper investigates the integrable structures of a specific third-order generalized Monge-Ampere equation, revealing Hamiltonian, symplectic, and recursion operators, and constructing infinite hierarchies of symmetries and conservation laws.

Contribution

It provides a comprehensive analysis of integrable structures for a generalized Monge-Ampere equation, including explicit operators and symmetry hierarchies, which was not previously established.

Findings

Identification of all integrable structures related to the equation

Construction of infinite hierarchies of symmetries and conservation laws

Explicit description of Hamiltonian, symplectic, and recursion operators

Abstract

We consider a 3rd-order generalized Monge-Ampere equation u_yyy - u_xxy^2 + u_xxx u_xyy = 0 (which is closely related to the associativity equation in the 2-d topological field theory) and describe all integrable structures related to it (i.e., Hamiltonian, symplectic, and recursion operators). Infinite hierarchies of symmetries and conservation laws are constructed as well.