Langrangian formulation and solitary wave solutions of a generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity in physical sciences and engineering

This paper presents analytical studies carried out explicitly on a higher-dimensional generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity arising in engineering and nonlinear science. We obtain analytic solutions for the underlying equation via Lie group approach as well as direct integration method. Moreover, we engage the extended Jacobi elliptic cosine and sine amplitude functions expansion technique to seek more exact travelling wave solutions of the equation for some particular cases. Consequently, we secure, singular and nonsingular (periodic) soliton solutions, cnoidal, snoidal as well as dnoidal wave solutions. Besides, we depict the dynamics of the solutions using suitable graphs. The application of obtained results in various fields of sciences and engineering are presented. In conclusion, we construct conserved currents of the aforementioned equation via Noether’s theorem (with Helmholtz criteria) and standard multiplier technique through the homotopy formula.