On the solution of homogeneous generalized wave equation

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.

Generalized solution of Sine-Gordon equation

In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.

On the Fundamental Solution of a Linearized Homogeneous Coagulation Equation

We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K (x, y) = (xy)λ/2, around the steady state f (x) = x−(3+λ)/2 with λ ∈ (1, 2). Detailed estimates on its asymptotics are obtained. Some consequences are deduced for the flux properties of the particles distributions described by such models.

On the Bifurcation of Traveling Wave Solution of Generalized Camassa-Holm Equation

The generalized Camassa-Holm equation ut + 2kux − uxxt + auux = 2uxuxx + uuxxx + γuxxx is considered in this paper. Under traveling wave variable substitution, the equation is related to a planar singular system. By making a transformation this singular system becomes a regular system. Through discussing the dynamical behavior of the regular system, the explicit periodic blow-up solutions and s...

On the solution of the generalized airfoil equation