Related papers: On the numerical solution of the Klein-Gordon equa…
We study soliton solutions to the Klein-Gordon equation via Lie symmetries and the travelling-wave ansatz. It is shown, by taking a linear combination of the spatial and temporal Lie point symmetries, that soliton solutions naturally exist,…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
The scattering problem for the Klein-Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein-Gordon equation we prove the existence of the scattering operator.
In this paper, we formulate and analyse a geometric low-regularity integrator for solving the nonlinear Klein-Gordon equation in the $d$-dimensional space with $d=1,2,3$. The integrator is constructed based on the two-step trigonometric…
A technique is described in this paper to avoid order reduction when integrating reaction-diffusion initial boundary value problems with explicit exponential Rosenbrock methods. The technique is valid for any Rosenbrock method, without…
This paper is concerned with the numerical approximation of the Dirichlet initial-boundary-value problem of nonlinear pseudo-parabolic equations with spectral methods. Error estimates for the semidiscrete Galerkin and collocation schemes…
In this paper, we study the nonrelativistic limit of the cubic nonlinear Klein-Gordon equation in $\mathbb{R}^{3}$ with a small parameter $0<\varepsilon \ll 1$, which is inversely proportional to the speed of light. We show that the cubic…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
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…
In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…
We make a rigorous study of classical field equations on a 2-dimensional signature changing spacetime using the techniques of operator theory. Boundary conditions at the surface of signature change are determined by forming self-adjoint…
The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the…
A high precision, and space time fully decoupled, wavelet formulation numerical method is developed for a class of nonlinear initial boundary value problems. This method is established based on a proposed Coiflet based approximation scheme…
In this paper, an efficient numerical technique for the time-fractional telegraph equation is proposed. The aim of this paper is to use a relatively new type of B-spline called the cubic trigonometric B-splines for the proposed scheme. This…
We prove the local well-posedness of the initial boundary value problem for the nonlinear quadratic Schr\"odinger equation under low initial-boundary regularity assumption via the boundary integral operator method introduced by…
The cubic Trigonometric B-spline(CTB) functions are used to set up the collocation method for finding solutions of the Burgers' equation. The effect of the CTB in the collocation method is sought by studying two text problems. The Burgers'…
We present and analyze two regularized finite difference methods which preserve energy of the logarithmic Klein-Gordon equation (LogKGE). In order to avoid singularity caused by the logarithmic nonlinearity of the LogKGE, we propose a…
The double-exponential Sinc-collocation method is known as a super-accurate method for solving initial value problems of ordinary differential equations, for which the error decreases almost exponentially as a function of the number of…
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies…
This work presents a collocation method for solving linear Fredholm integral equations of the second kind defined on a closed contour in the complex plane. The right-hand side of the equation is a piecewise continuous function that may have…