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Conservation laws and optimal system of extended quantum Zakharov-Kuznetsov equation. (English) Zbl 1420.35071

Summary: In this paper, the \((2+1)\)-dimensional extended quantum Zakharov-Kuznetsov equation is further explored. The equation is shown to be self-adjoint and conserved vector is constructed according to the related theorem. Then the corresponding optimal system of one-dimensional subgroups is determined. Similarity reductions of the equation under optimal system of subgroups are performed. As a result, the \((2+1)\)-dimensional extended quantum Zakharov-Kuznetsov equation is reduced into a linear PDE with two independent variables.

MSC:

35G20 Nonlinear higher-order PDEs
35L65 Hyperbolic conservation laws
58J70 Invariance and symmetry properties for PDEs on manifolds
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