Symmetry analysis for the $2+1$ generalized quantum Zakharov-Kuznetsov equation

Abstract

We solve the group classification problem for the $2+1$ generalized quantum Zakharov-Kuznetsov equation. Particularly we consider the generalized equation $u_t+f\left(u\right)u_z+u_{zzz}+u_{xxz}=0$, and the time-dependent Zakharov-Kuznetsov equation $u_t+\delta \left(t\right)u{u}_z+\lambda \left(t\right)u_{zzz}+\epsilon \left(t\right)u_{xxz}=0$% . Function $f\left(u\right)$ and $\delta \left(t\right),\lambda \left(t\right)$,~$\epsilon \left(t\right)$ are determine in order the equations to admit additional Lie symmetries.\ Finally, we apply the Lie invariants to find similarity solutions for the generalized quantum Zakharov-Kuznetsov equation.

13 pages, 9 tables, no figures

References in corpus (1)

• Solutions of quasi-geostrophic turbulence in multi-layered configurations