Periodic, solitary and rational wave solutions of the 3D extended quantum Zakharov-Kuznetsov equation in dense quantum plasmas. (English) Zbl 1231.76362

Summary: The three-dimensional extended quantum Zakharov-Kuznetsov (ZK) equation was investigated in dense quantum plasmas which arises from the dimensionless hydrodynamics equations describing the nonlinear propagation of the quantum ion-acoustic waves. With the aid of symbolic computation, many types of new analytical solutions of the extended quantum ZK equation are constructed in terms of some powerful ansatze, which include new doubly periodic wave, solitary wave, shock wave, rational wave, and singular wave solutions. Moreover, we analyze the nonlinear wave propagation of the obtained solutions for some chosen parameters.


76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35C07 Traveling wave solutions
35C08 Soliton solutions
76B25 Solitary waves for incompressible inviscid fluids
Full Text: DOI


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