Abstract
•Applications of mathematical physics models.•The hydrodynamic mathematical methods.•First integro-differential KP hierarchy equation.
In this manuscript, three novel schemes (Generalized direct algebraic; Improved simple equation and Modified F-expansion methods) are successfully utilized to find the solitary solutions of generalized form of Pochhammer-Chree equation.The concerned wave model has been used in the scrutiny for the propagating of harmonic waves in a cylindrical rod and several problems in fluid mechanics and waves theory in physics. The obtained results have imperative role in the field of the nonlinear science.