Symmetric $q$-deformed KP hierarch

Abstract

Based on the analytic property of the symmetric $q$-exponent $e_q(x)$, a new symmetric $q$-deformed Kadomtsev-Petviashvili ($q$-KP) hierarchy associated with the symmetric $q$-derivative operator ${\partial }_q$ is constructed. Furthermore, the symmetric $q$-CKP hierarchy and symmetric $q$-BKP hierarchy are defined. Here we also investigate the additional symmetries of the symmetric $q$-KP hierarchy.

11pages, accepted by Chinese Annals of Mathematics Series B(2014)

References in corpus (1)

• Virasoro and W-constraints for the $q$-KP hierarchy