In contrast, the self-gravitational counterparts grow as bell-shaped rarefactive soliton-like structures (conservative). The correlative effect of diverse plasma parameters on the amplitudes and patterns is explicitly investigated. Interestingly, this is conjectured that the grain-mass plays a key role in the eigenmode shaping (growth and decay) through the interplaying processes of pulsating gravito-electrostatic coupling. As the grain-mass increases, a new type of shock-to-soliton transition results, and so forth. The significance of the study in space, laboratory and astrophysical environments is stressed. | Communications in Physics, Vol. 24, No. 1 (2014), pp. 45-67 NEW ASPECTS ON STABILITY ANALYSIS OF A PLANAR CHARGE-VARYING COLLISIONAL DUST MOLECULAR CLOUD WITH FINITE THERMAL INERTIA P. K. KARMAKAR AND B. BORAH Department of Physics, Tezpur University, Napaam-784028, Tezpur, Assam, India E-mail: pkk@ Received 19 August 2013 Accepted for publication 24 December 2013 Abstract. A theoretical evolutionary model for the nonlinear stability analysis of a planar dust molecular cloud (DMC) in quasi-neutral hydrodynamic equilibrium on the Jeans scales of space and time is developed. It is based on a selfgravitating multi-fluid model consisting of the warm electrons and ions, and the inertial cold dust grains with partial ionization. The Jeans assumption of self-gravitating uniform medium is adopted for fiducially analytical simplification by neglecting the zero-order field. So, the equilibrium is justifiably treated initially as “homogeneous”, thereby validating nonlinear local analysis. The lowest-order finite inertial correction of the thermal species (thermal inertia, which is conventionally neglected), heavier grain-charge fluctuation and all the possible collisional dynamics are included simultaneously amid non-equilibrium plasma inhomogeneities. We apply a standard multiple scaling technique methodologically to show that the eigenmodes are collectively governed by a new electrostatic driven Korteweg-de Vries (d-KdV) equation having a self-consistent nonlinear driving source, and self-gravitational Korteweg-de Vries (KdV) equation with neither a source, nor a sink. A detailed numerical shape-analysis with judicious multi-parameter variation parametrically portrays the excitation of electrostatic eigenmodes evolving as damped oscillatory shocks (nonconservative) with the increasing global amplitude due to the source, and extended two-tail compressive solitons (conservative), when the source-strength becomes very weak. In contrast, the self-gravitational .
