Exact solutions of a quintic dispersive equation. (December 2022) - Iqbal, Anjum; Naeem, Imran
Abstract: We present novel exact solutions for a class of Rosenau's quintic dispersive equations. The variational derivative approach is employed to construct conservation laws for a slightly generalized version of the quintic equation. The double reduction theory, based on the association of symmetries and conservation laws, is utilized to obtain a fourth-order nonlinear ODE, which is then solved to compute exact solutions of the quintic equation. In particular, the G ′ G -expansion method for the reduced fourth-order nonlinear ODE is applied to construct new exact solutions of the quintic PDE with a cubic nonlinearity. Highlights: A generalized version of Rosenau's quintic dispersive equation is considered. Conservation Laws of the quintic equation are derived using the multiplier method. Novel exact solutions are procured from the derived conservation laws. The double reduction theory is utilized. The resulting solutions represent solitons and compactons.