Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation

Concentration Compactness for the Critical Maxwell-klein-gordon Equation

We prove global regularity, scattering and a priori bounds for the energy critical MaxwellKlein-Gordon equation relative to the Coulomb gauge on (1 + 4)-dimensional Minkowski space. The proof is based upon a modified Bahouri-Gérard profile decomposition [1] and a concentration compactness/rigidity argument by Kenig-Merle [5], following the method developed by the first author and Schlag [10] in...

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

B-SPLINE COLLOCATION APPROACH FOR SOLUTION OF KLEIN-GORDON EQUATION

We develope a numerical method based on B-spline collocation method to solve linear Klein-Gordon equation. The proposed scheme is unconditionally stable. The results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. Easy and economical implementation is the strength of this approach.  

Nonlinear Klein-Gordon Equation

An extended ( ′ G )–expansion method is obtained by improving the form of solution in ( G′ G )– expansion method which is proposed in recent years. By using the extended ( ′ G )–expansion method and with the aid of homogeneous balance principle, many explicit and exact travelling wave solutions with two arbitrary parameters to the Klein-Gordon equation are presented, including the hyperbolic so...