Convective Vector Wave Equation of Aeroacoustics

Wave-vector field of convective flow patterns.

The convective Cahn-Hilliard equation

We consider the convective Cahn–Hilliard equation with periodic boundary conditions as an infinite dimensional dynamical system and establish the existence of a compact attractor and a finite dimensional inertial manifold that contains it. Moreover, Gevrey regularity of solutions on the attractor is established and used to prove that four nodes are determining for each solution on the attractor...

Optimal control of convective FitzHugh-Nagumo equation

We investigate smooth and sparse optimal control problems for convective FitzHughNagumo equation with travelling wave solutions in moving excitable media. The cost function includes distributed space-time and terminal observations or targets. The state and adjoint equations are discretized in space by symmetric interior point Galerkin (SIPG) method and by backward Euler method in time. Several ...

Numerical solution of the wave equation using shearlet frames

In this paper, using shearlet frames, we present a numerical  method  for solving  the wave equation. We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.

On the Spectral Stability of Solitary Wave Solutions of the Vector Nonlinear Schrödinger Equation

We consider a system of coupled cubic nonlinear Schrödinger (NLS) equations i ∂ψj ∂t = − ∂ψj ∂x2 + ψj n ∑ k=1 αjk|ψk| j = 1, 2, . . . , n, where the interaction coefficients αjk are real. The spectral stability of solitary wave solutions (both bright and dark) is examined both analytically and numerically. Our results build on preceding work by Nguyen et al. and others. Specifically, we present...