Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg-de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma

In this research work, we investigate the dust ion-acoustic solitary wave in an unmagnetized collisional dusty plasma, which consists on ions having positive charge, dust fluid with negative charge, q nonextensive electrons and background neutral particles. We formulated nonlinear model by the damped modified Korteweg-de Vries (D-mKdV) equation by applying reductive perturbation technique. We also constructed the new solitary wave solutions for nonlinear D-mKdV equation with the help of two techniques. The obtained solutions are new and general and having the structure in the form of solitons, kink and antikink wave solitons, traveling waves, periodic solitary wave and we also show the structure of obtained solutions by two-dim and three-dim graphical by using the Mathematica to know the physical interpretation of different structure of DIASWs. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of fluid, problems of biomedical, dynamics of adiabatic parameters, industrial phenomena and many other branches. The calculations show that these techniques are more effective, fruitfulness and powerful to investigate analytical other nonlinear physical models of PDEs involves in Mathematical physics, plasma physics, Geo physics, fluid mechanics, hydrodynamics, mathematical biology, field of engineering and many other physical sciences. (C) 2019 Elsevier B.V. All rights reserved.