On new conservative aspects of a derived d-KdV equation in transonic plasma

A linear source driven non-linear dynamical evolution system governed by the d-KdV equation of our present concern arises in the following form with all usual notations in the theoretical description of the non-linear normal mode behaviour of plasma ion acoustic mode through transonic plasma of an assumed finite extension. The ion acoustic wave-induced lowest order perturbed potential in transonic plasma equilibrium configuration can be written in a normalized form as the following Motivated by the search for the explicit forms of all the possible conservation laws realistically applicable under a defined transonic plasma equilibrium, it is mathematically modelled into the repeated hydrodynamically standard form of fluid flux conservation construct , where associated conserved density and associated conserved flux vanish asymptotically at . In the present contribution a large number of conservation laws of applied mathematical significance associated with the d-KdV flow dynamics followed by realistic physical discussions are presented in transonic plasma domain. A detailed numerical analysis for our d-KdV profiles and corresponding phase space portraits methodologically carried out for the first time to investigate its geometries in the defined transonic plasma equilibrium configuration.