This work was devoted to the study of a relaxation limit so-called aggregation equation with pointy potential in one-dimensional space. The is today widely used model dynamics density individuals attracting each other through potential. When this pointy, solutions are known blow up final time. For reason, measure-valued have been defined. In paper, we investigated an approximation such thanks s...

We construct a kind of thermal potential and then put the black hole thermodynamic system in it. In this regard, some properties are related to geometric characteristics potential. Driven by intrinsic fluctuations, behavior is stochastic. With help solving Fokker-Planck equation analytically, we obtain discrete energy spectrum Schwarzschild Banados-Teitelboim-Zanelli (BTZ) holes For hole, propo...

Soliton motion in some external potentials is studied using the nonlinear Schrödinger equation. Solitons are scattered by a potential wall. Solitons propagate almost freely or are trapped in a periodic potential. The critical kinetic energy for reflection and trapping is evaluated approximately with a variational method. keywords: soliton, nonlinear Schrödinger equation, Lagrangian The nonlinea...