Related papers: The zero mass problem for Klein-Gordon equations: …
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the…
This work focuses on the emergence of dark phases (dark energy-induced phases) in the radial wave function of scalar particles. We achieve this by presenting novel solutions to the Klein-Gordon equation in a spherically symmetric spacetime,…
We consider the decay rate of solutions to nonlinear Klein-Gordon systems with a critical type nonlinearity. We will specify the optimal decay rate for a specific class of Klein-Gordon systems containing the dissipative nonlinearites. It…
We consider general semilinear, multispeed Klein-Gordon systems in space dimension two with some non-degeneracy conditions. We prove that with small initial data such solutions are always global and scatter to a linear solution. This result…
The analytical solutions of the Klein-Gordon equation with the Yukawa potential is presented within the framework of an approximation to the centrifugal potential for any arbitrary state with the position-dependent mass using the parametric…
We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations…
In this paper it is shown that an equivalent to the complex Klein-Gordon equation can be obtained from the (2+3) dimensional Einstein equations coupled to a conserved energy momentum tensor. In an explicit toy model we give matching…
Starting from relativistic mass-less Madelung fluid, we shall develop a class of typical wave functions by imposing it to maximize Shannon entropy given its finite average quantum potential. We show that there is a class of solutions in…
We briefly summarize the most relevant steps in the search of rigorous results about the properties of quantum systems made of three bosons interacting with zero-range forces. We also describe recent attempts to solve the unboundedness…
In this paper, we give a formulation of the variational iteration method that makes it suitable for the analysis of the solutions of Klein-Gordon equations with variable coefficients. We particularly study a Klein-Gordon problem which has…
In the paper, for the 3D quasilinear Klein-Gordon equation with the small initial data posed on the product space $\mathbb{R}^{2}\times \mathbb{T}$, we focus on the lower bound of the lifespan of the smooth solution. When the size of…
The substratum for physics can be seen microscopically as an ideal fluid pierced in all directions by the straight vortex filaments. Small disturbances of an isolated filament are considered. The Klein-Gordon equation without mass…
We consider the PDEs version of the Carleson problem in the context of the cubic nonlinear Klein-Gordon equation. This means that we aim to establish the lowest regularity class for which one has almost everywhere pointwise convergence of…
We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity \begin{equation*} \partial_{t}^{2}u-\partial_{x}^{2}u+u-|u|^{p-1}u+|u|^{q-1}u=0,\quad \mbox{on}\ [0,\infty)\times…
We consider the initial value problem for a system of cubic nonlinear Schr\"odinger equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude…
It has been shown in [Yang-Yu 2019] that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space $\mathbb{R}^{1+3}$ decay like linear solutions. One hence can define the associated…
We study the non-uniqueness sets for solutions to the Klein-Gordon equation in 1 space dimension, for solutions whose Fourier transform is a finite complex measure absolutely continuous with respect to arc length. We show that generally, in…
In this paper the stationary Klein-Gordon equation is considered for the Coulomb potential in non-commutative space. The energy shift due to noncommutativeity is obtained via the perturbation theory. Furthermore, we show that the degeneracy…
We study the focusing, cubic, nonlinear Klein-Gordon equation in 3D with large radial data in the energy space. This equation admits a unique positive stationary solution, called the ground state. In 1975, Payne and Sattinger showed that…
We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground…