Abstract
.In this article we studied analytically the propagation of nonlinear ion acoustic solitary waves modeled by the generalized Schamel (GS) equation arising in plasma physics using auxiliary equation mapping method. As a result, we found a series of more general and new families of solutions, which are more powerful in the development of soliton dynamics, quantum plasma, adiabatic parameter dynamics, biomedical problems, fluid dynamics, industrial studies and many other fields. The calculations prove that this method is more reliable, straightforward, and effective to study analytically other nonlinear complicated physical problems modeled by complex nonlinear partial differential equations arising in mathematical physics, hydrodynamics, fluid mechanics, mathematical biology, plasma physics, engineering disciplines, chemistry and many other natural sciences. We also have expressed our solutions graphically with the help of Mathematica 10.4 to understand physically the behavior of different shapes of ion acoustic solitary waves including kink-type, anti-kink-type, half-bright and dark soliton.