A. Mahdipour-Shirayeh

arXiv2010

Preliminary group classification for generalized inviscid Burger's equation

Preliminary group classification for a class of generalized inviscid Burger's equations in the general form $u_t+g(x, u)u_x = f(x, u)$ is given and additional equivalence transformations are found. Adduced results complete and essentially generalize recent works on the subject . A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. The result of the work is a wide class of equations summarized in table form.

math.DG↗

arXiv2008

Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.

physics.flu-dyn↗