Integrable systems from supergravity BPS equations

TL;DR

This paper demonstrates that certain integrable systems derived from supergravity BPS equations are part of an infinite family, each associated with a function, and can be linearized and solved explicitly.

Contribution

It introduces a broad class of integrable systems from supergravity equations, showing they can all be mapped to linear equations for explicit solutions.

Findings

Integrable systems from supergravity are part of an infinite family.

Each system can be linearized and solved explicitly.

Solutions depend on an arbitrary real function.

Abstract

Integrable systems of the sine-Gordon/Liouville type, which arise from reducing the BPS equations for solutions invariant under 16 supersymmetries in Type IIB supergravity and M-theory, are shown to be special cases of an infinite family of integrable systems, parametrized by an arbitrary real function $f$ of a real variable. It is shown that, for each function $f$, this generalized integrable system may be mapped onto a system of linear equations, which in turn may be integrated in terms of the two linearly independent solutions of an ordinary linear second order differential equation which depends only on the function $f$.