We survey existence and regularity results for semi-linear wave equations. In particular, we review the recent regularity results for the u5-Klein Gordon equation by Grillakis and this author and give a self-contained, slightly simplified proof.

In this paper, two solitary wave solutions are obtained for the Coupled Klein-Gordon-Schrodinger and Coupled quadratic nonlinear equations by the ansatz method. Both topological and non-topological solitary wave solutions are obtained.

In this paper we construct the autonomous quad-equations which admit as symmetries five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained are classified up point transformations some simple non-autonomous transformations. We discuss our results in framework of literature. There among them a few new examples both sine-Gordon Liou...

The strong instability of ground state standing wave solutions eφω(x) for nonlinear Klein-Gordon equations has been known only for the case ω = 0. In this paper we prove the strong instability for small frequency ω.

A relativistic extension of our pseudo-shifted l–expansion technique is presented to solve for the eigenvalues of Dirac and Klein-Gordon equations. Once more we show the numerical usefulness of its results via comparison with available numerical integration data.

By exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mass. §

We show propositions in favour of relations between the phase space of 3D gravity, moduli of quasi-Fuchsian groups, global solutions of cosh-Gordon equations and minimal surfaces in hyperbolic spaces.

We prove the global well-posedness and we study the linear response for a system of two coupled equations composed of a Dirac equation for an infinite rank operator and a nonlinear wave or Klein-Gordon equation.