Solutions for real dispersionless Veselov-Novikov hierarchy

TL;DR

This paper explores the real dispersionless Veselov-Novikov hierarchy, utilizing symmetry constraints, Faber polynomials, and hodograph transformations to derive exact solutions and analyze conserved densities.

Contribution

It introduces a novel approach combining symmetry reductions, Faber polynomials, and hodograph methods to solve the real dispersionless Veselov-Novikov hierarchy.

Findings

Conserved densities relate to Faber polynomials and can be computed recursively.

Exact solutions of the dVN hierarchy are obtained using hodograph transformations.

Symmetry constraints help simplify and solve the dispersionless equations.

Abstract

We investigate the dispersionless Veselov-Novikov (dVN) equation based on the framework of dispersionless two-component BKP hierarchy. Symmetry constraints for real dVN system are considered. It is shown that under symmetry reductions, the conserved densities are therefore related to the associated Faber polynomials and can be solved recursively. Moreover, the method of hodograph transformation as well as the expressions of Faber polynomials are used to find exact real solutions of the dVN hierarchy.