Abstract
The nonlinear propagation of dust-ion acoustic solitary waves and shocks can be represented by a nonlinear evolution partial differential equation, namely the perturbed $$(3+1)$$-dimensional Zakharov–Kuznetsov (pZK) equation. Based on some subalgebras of symmetries, several reductions and many group-invariant solutions are found for the pZK equation. One of the reduced partial differential equations is dealt using new generalized exponential rational function method which was proposed by Ghanbari and Inc (Eur. Phys. J. Plus 133: 142, 2018), to obtain closed-form analytical solutions. Obtained solutions are new solitary wave, multi-soliton and kink type which is significant in the field of plasma physics.
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