Related papers: Slightly Two or Three Dimensional Self-Similar Sol…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
The particle emission in relativistic hydrodynamic model is formulated assuming a sharp 3-dimensional space-time freeze-out hypersurface. The boundary conditions correspond to the energy-momentum and charge conservation between fluid and…
The smoothed particle hydrodynamics (SPH) method has been increasingly used to study fluid problems in recent years; but its computational cost can be high if high resolution is required. In this study, an adaptive resolution method based…
We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically simmetric space--time. We match a very simple solution to the symmetry equations with the exterior one (Vaidya). We…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…
In this paper we consider the multi-dimensional Quantum Hydrodynamics (QHD) system, by adopting an intrinsically hydrodynamic approach. The present work continues the analysis initiated in [6] where the one dimensional case was studied.…
A higher-order dispersive equation is introduced as a candidate for the governing equation of a field theory. A new class of solutions of the three-dimensional field equation are considered, which are not localized functions in the sense of…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing…
Self-similar shock solutions in spherically symmetric polytropic gas flows are constructed and analyzed in contexts of proto-star formation processes. Among other possible solutions, we model a similarity shock across the sonic critical…
Radially symmetric shadow wave solutions to the system of multidimensional pressureless gas dynamics are introduced, which allow one to capture concentration of mass. The transformation to a one-dimensional system with source terms is…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
We study solutions of the relativistic hydrodynamical equations, which describe spherical or cylindrical expansion of ideal fluid. We derived approximate solutions involving two arbitrary functions, which describe asymptotic behavior of…
A new class of accelerating, exact and explicit solutions of relativistic hydrodynamics is found - more than 50 years after the previous similar result, the Landau-Khalatnikov solution. Surprisingly, the new solutions have a simple form,…
For a wide variety of initial and boundary conditions, adiabatic one dimensional flows of an ideal gas approach self-similar behavior when the characteristic length scale over which the flow takes place, $R$, diverges or tends to zero. It…
We describe fireballs that rehadronize from a perfectly fluid quark matter to a chemically frozen, multi-component hadron gas. In the hydrodynamics of these fireballs, we utilize the lattice QCD equation of state, however, we also apply…
We construct solutions of Schr\"odinger equations which are asymptotically self-similar solutions as time goes to infinity. Also included are situations with two bubbles. These solutions are global, with non-zero $L^2$ norms, and are…
The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a…
Spiral wave solutions are found in linear and weakly nonlinear irrotational water wave equations. These unsteady spiral waves evolve from suitable initial conditions; they are not induced by external forcing. In the linear case, a long-time…
The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small…