Related papers: Solving nonlinear Klein-Gordon equation with non-s…
It is well known that for the quasilinear Klein-Gordon equation with quadratic nonlinearity and sufficiently decaying small initial data, there exists a global smooth solution if the space dimensions $d\geq2$. When the initial data are of…
We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully…
Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with…
In this article, we study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we…
We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities $Q_0$ and $Q_{\alpha\beta}$. The main result states that the solution to the 2D coupled systems exists globally provided that the initial data are small…
Minimal length of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of…
Despite the fact that it is not integrable, the 1 + 2-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N greater than or equal to 1. Based on these solutions, a…
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…
We initiate the study of the asymptotic behavior of small solutions to one-dimensional Klein-Gordon equations with variable coefficient quadratic nonlinearities. The main discovery in this work is a striking resonant interaction between…
New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional…
We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a…
In this paper, we build a Gibbs measure for the 1d cubic Klein-Gordon equation on $\mathbb R$ with a decreasing non linearity, in the sense that the non linearity $f^3$ is multiplied by $\chi$ where $\chi$ is a sufficiently integrable non…
We establish improved uniform error bounds on time-splitting methods for the long-time dynamics of the nonlinear Klein--Gordon equation (NKGE) with weak cubic nonlinearity, whose strength is characterized by $\varepsilon^2$ with $0 <…
The solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions $a,b,A,B$. The functions $a(k)$ and $b(k)$ are…
The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the…
We study the the nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity. In particular, we consider an order-$r$ normalized approximation of NLKG (which…
In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It is based on a suitable…
The sine-Gordon equation is a nonlinear partial differential equation. It is known that the sine-Gordon has soliton solutions in the 1D and 2D cases, but such solutions are not known to exist in the 3D case. Several numerical solutions to…
We consider the U(1)-invariant nonlinear Klein-Gordon equation in discrete space and discrete time, which is the discretization of the nonlinear continuous Klein-Gordon equation. To obtain this equation, we use the energy-conserving…
In this thesis we explore S. Klainerman's proof on the global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, as established in his paper from 1985. We consider initial data with…