Multi-component decompositions, linear superpositions, and new nonlinear integrable coupled KdV-type systems

TL;DR

This paper explores how decompositions of nonlinear integrable systems enable linear superposition solutions and the construction of new coupled KdV-type systems that are not decoupled by variable changes.

Contribution

It introduces multi-component decompositions of the potential BKP hierarchy to generate new nonlinear integrable coupled systems and superposition solutions.

Findings

Linear superpositions of solutions satisfy the same equations.

New nonlinear coupled KdV-type systems are constructed.

Multi-component decompositions lead to systems not decoupled by variable changes.

Abstract

The existence of decompositions of the nonlinear integrable systems not only permits us to establish so-called linear superposition solutions but also to derive new nonlinear integrable coupled systems. Restricting our attention to the single component decompositions of the potential BKP hierarchy, we obtain that suitable linear superpositions of some decomposition solutions still satisfy the same equations. In parallel, successful attempts are made by multi-component decompositions of the potential BKP hierarchy to construct linear superposition solutions and new nonlinear integrable coupled KdV-type systems that a change of dependent variables cannot decouple.