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Growth rate of transverse instabilities of solitary pulse solutions to a family of modified Zakharov-Kuznetsov equations. (English) Zbl 1220.76080
Summary: Using the small-$k$ expansion method, we obtain a closed-form expression for the growth rate of long-wavelength transverse instabilities of solitary pulse solutions to a modified Zakharov-Kuznetsov equation with a nonlinearity of the form $(Au^{p}+Bu^{2p})u_{x}$.

76X05Ionized gas flow in electromagnetic fields; plasmic flow
35Q35PDEs in connection with fluid mechanics
35Q51Soliton-like equations
76E25Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
Full Text: DOI
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