We address the dusty wind problem, from the point where dust formation has been completed and outward. Given grain properties, both radiative transfer and hydrodynamics components of the problem are fully defined by four additional input parameters. The wind radiative emission and the shape of its velocity profile are both independent of the actual magnitude of the velocity and are determined b...

We study the self-similar solutions for nonlinear Schrödinger type equations of higher order with nonlinear term |u|u by a scaling technique and the contractive mapping method. For some admissible value α, we establish the global well-posedness of the Cauchy problem for nonlinear Schrödinger equations of higher order in some nonstandard function spaces which contain many homogeneous functions. ...

We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold gas. The pressure, p, and energy-density, μ, in the shock-heated matter are assumed to obey p = wμ, where w is a positive constant. Consistent solutions are fou...

The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property results in great simplification of the governing partial differential equations. In addition, some self-similar solutions can describe the asymptotic behavio...