New Self - Similar Solutions of theNonlinear

Self-similar solutions‎ ‎of the Riemann problem for two-dimensional systems of conservation‎ ‎laws

In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem

On a Parallel Time - domain Method for theNonlinear Bla k - S holes

On Black-Scholes equation; method of Heir-equations‎, ‎nonlinear self-adjointness and conservation laws

In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

انبساط خود- مشابه پلاسماهای دارای یون‌های گرم به خلاء

Expansion of one dimensional collisionless plasma into vacuum is studied under different initial ions temperature. In this study, a simulation code is used, in which the electrons dynamic is determined by Vlasov equation and the ions dynamic is determined  by fluids equations. Finally, the effect of initial ions temperature on the expansion of plasma into vacuum is investigated and the obtained...

New Self-Similar Solutions of Polytropic Gas Dynamics

We explore semi-complete self-similar solutions for the polytropic gas dynamics involving self-gravity under spherical symmetry, examine behaviours of the sonic critical curve, and present new asymptotic collapse solutions that describe ‘quasi-static’ asymptotic behaviours at small radii and large times. These new ‘quasi-static’ solutions with divergent mass density approaching the core can hav...