Hamiltonian-Based Solutions of Certain PDE in Plasma Flows

The evolution nonlinear partial differential equations give an insight into the physical, mechanical, thermal, electrical and electro-mechanical behaviour of a nonlinear system. The study of these evolution equations and their solutions, especially in plasma transport through magnetic field lines, is essential to understand important principles applicable for transportation of plasma, such as magnetized plasma diffusion. It also has application to the sources of plasma which work at low temperature and pressure. One such PDE is the modified Kdv–Zakharov–Kuznetsov equation. These equations have solutions that are best described by solitons, kinks and periodic wave-type travelling wave solutions. The Hamiltonian- and the rational trigonometric method-based travelling wave solutions of these evolution equations are obtained. These solutions are also comparable with semi-analytical approaches such as tanh method, exp-function method, Jacobi elliptic function method, Jacobi theta function method, and numerical approaches such as Pertrov–Galerkien method and radial basis function method. The solutions obtained here are compared with the recent work by extended mapping method and Jacobi elliptic method and \(\frac{{G^{\prime}}}{G}\) method.