Integrable pseudopotentials related to generalized hypergeometric functions

TL;DR

This paper constructs integrable pseudopotentials using generalized hypergeometric functions, leading to new integrable systems in (2+1) and (1+1) dimensions, expanding the understanding of hydrodynamic type systems.

Contribution

It introduces a novel method to generate integrable pseudopotentials with arbitrary fields based on generalized hypergeometric functions, creating new classes of hydrodynamic systems.

Findings

Developed integrable pseudopotentials for multiple fields

Generated new (2+1)-dimensional hydrodynamic systems

Produced integrable (1+1)-dimensional systems

Abstract

We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic type systems. An interesting class of integrable (1+1)-dimensional hydrodynamic type systems is also generated by our pseudopotentials.