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arXiv · 2107.01647

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

Andronikos Paliathanasis·P. G. L. Leach
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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 $u_{t}+δ\left( t\right) uu_{z}+λ\left( t\right) u_{zzz}+\varepsilon \left( t\right) u_{xxz}=0$% . Function $f\left( u\right) $ and $δ\left( t\right) ,~λ\left( t\right) $,~$\varepsilon \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.

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Andronikos Paliathanasis, P. G. L. Leach. 2021-07-04. Symmetry analysis for the $2+1$ generalized quantum Zakharov-Kuznetsov equation. https://doi.org/10.1088/1402-4896%2Fac0dff

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