Related papers: Some sharp null-form type estimates for the Klein-…
We analyse the complex-valued Klein-Gordon Equation from an integrability perspective by the implementation of the Lie Theory of Continuous Groups, where this equation is governed by power-law nonlinearity. We write the equations in terms…
We study the Klein-Gordon equation with general interaction term, which may be linear or nonlinear, and space-time dependent. The initial data is general, large and non-radial. We prove that global solutions are asymptotically given by a…
We derive an extended cubic-quintic nonlinear Schr\"{o}dinger equation with Hamiltonian structure in a nonlinear Klein-Gordon model with cubic-quintic nonlinearity. We use the nonlinear dispersion relation to properly take into account the…
A system of coupled kinetic transport equations for the Wigner distributions of a free variable mass Klein-Gordon field is derived. This set of equations is formally equivalent to the full wave equation for electromagnetic waves in…
The discrete Klein-Gordon equation on a two-dimensional square lattice satisfies an $\ell^1 \mapsto \ell^\infty$ dispersive bound with polynomial decay rate $|t|^{-3/4}$. We determine the shape of the light cone for any choice of the mass…
In this paper, we investigate the nonlinear Klein-Gordon equation on a metric star graph with three semi-infinite bonds. At the branching point, we impose a weighted continuity condition and a generalized weighted Kirchhoff condition for…
In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by $e^{it\phi(\sqrt{-\Delta})}$, where $\phi: \mathbb{R}^+\to \mathbb{R}$ is smooth away from the origin. Especially, the decay…
We study linear Klein-Gordon equations with moving potentials motivated by the stability analysis of traveling waves and multi-solitons. In this paper, Strichartz estimates, local energy decay and the scattering theory for these models are…
We give blow-up results for the Klein-Gordon equation and other perturbations of the semilinear wave equations with superlinear power nonlinearity, in one space dimension or in higher dimension under radial symmetry outside the origin.
The purpose of this article is twofold. First we give a very robust method for proving sharp time decay estimates for the most classical three models of dispersive Partial Differential Equations, the wave, Klein-Gordon and Schr{\"o}dinger…
We are interested in establishing stability results for a system of semilinear wave and Klein-Gordon equations with mixed coupling nonlinearities, that is, we consider all of the possible quadratic nonlinear terms of the type of wave and…
Numerical simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime are performed. We use two structure-preserving discrete forms of the Klein--Gordon equation. The disparity between the two forms is the discretization…
We prove a completeness result for a class of polynomial solutions of the wave equation called wave polynomials and construct generalized wave polynomials, solutions of the Klein-Gordon equation with a variable coefficient. Using the…
We deal with fixed-time and Strichartz estimates for the Schr\"odinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical…
We introduce a family of high-order time semi-discretizations for semilinear wave equations of Klein--Gordon type with arbitrary smooth nonlinerities that are uniformly accurate in the non-relativistic limit where the speed of light goes to…
We construct the causal (forward/backward) propagators for the massive Klein-Gordon equation perturbed by a first order operator which decays in space but not necessarily in time. In particular, we obtain global estimates for…
Inspired by the forms of delay-Painleve equations, we consider some new differential-discrete systems of KdV, mKdV and Sine-Gordon - type related by simple one way Miura transformations to classical ones. Using Hirota bilinear formalism we…
We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular…
In this paper, we study the long time behavior of energy solutions for a class of wave equation with time-dependent mass and speed of pro\-pagation. We introduce a classification of the potential term, which clarifies whether the solution…
We investigate the effect of the breaking of integrability in the integrals of motion of a sine-Gordon-like system. The class of quasi-integrable models, discussed in the literature, inherits some of the integrable properties they are…