Quantum field theory of a damped vibrating string as the simplest dissipative scalar field investigated by its coupling with an infinit number of Klein-Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to velocity obtained for a special choice of coupling function and quantum dynamics for such a dissipative ...

Numerical technique Lattice Boltzmann Method (LBM) is relatively new approach based on gas kinetic theory in meso-scale. Macroscopic variables such as pressure and velocity can be determined by momentum of so called particle distribution functions which are described by Boltzmann transport equation. LBM has been extensively studied in last several decades and witnessed as capable like conventio...

General rogue waves in the Davey–Stewartson (DS)II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background in a line profile and then retreat back to the constant background again. It is also shown that multi-rogue waves describe the intera...

Our starting point is a selection-mutation equation describing the adaptive dynamics of a quantitative trait under the influence of an ecological feedback loop. Based on the assumption of small (but frequent) mutations we employ asymptotic analysis to derive a Hamilton-Jacobi equation. Well-established and powerful numerical tools for solving the Hamilton-Jacobi equations then allow us to easil...

The paper gives an explicit representation of the Green’s function Dirichlet boundary value problem for polyharmonic equation in unit ball. solution homogeneous is found. An example solving with simplest polynomial right-hand side given.

In this talk, we will introduce high accurate numerical schemes for solving forward backward stochastic differential equations (FBSDEs) with jumps. In these schemes, the simplest Euler scheme with only one jump is used to solve the forward stochastic differential equation (SDE), and multistep schemes is used to solve the backward stochastic differential equation (BSDE) with high convergence rat...

We consider solutions to the complex Trkalian equation, ~ ∇×~c = ~c, where ~c is a 3 component vector function with each component in the complex field, and may be expressed in the form ~c = e ~ ∇F, with g real and F complex. We find, there are precisely two classes of solutions; one where g is a Cartesian variable and one where g is the spherical radial coordinate. We consider these flows to b...