We establish the existence of global Lipschitz continuous weak entropy solutions to the Cauchy problem for a class of quasilinear wave equations with an external positional force. We prove the consistency and the convergence of uniformly bounded nite{diierence fractional step approximations. Therefore the uniform bound is shown to hold for globally Lipschitz continuous external forces.

We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive Sq entropies. Our present contribution is in line with recent developments, where nonlinear extensions inspired on the q-thermostatistical formalism have been proposed for the Schroedinger, Klein–Gordon, and Dirac wave equations. These previously introduced equati...

The purpose of this article is twofold. First we give a very robust method for proving sharp time-decay estimates the three most classical models dispersive partial differential equations—the wave, Klein–Gordon, and Schrödinger equations, on curved geometries—showing under general assumptions exact same decay as Euclidean case. Then extend these properties to case boundary value problems.

The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. In this study, the library 2DECOMP&FFT is used in a Fourier spectral scheme to solve the Klein-Gordon equation and strong scaling of the code is examined on thirteen different machi...

We show that the black hole perturbations of the Hayward static solution to the massless Einstein-Klein-Gordon equations are actually gauge artifacts resulting from the linearization of a coordinate transformation. In a recent paper [1], Hayward discussed a homothetic, static solution to the massless Einstein-Klein-Gordon equations. With the spherically symmetric ansatz ds = rdΩ − 2edxdx (1) (w...

The Faddeev-Reshetikhin procedure corresponds to a removal of the nonultralocality of the classical SU(2) principal chiral model. It is realized by defining another field theory, which has the same Lax pair and equations of motion but a different Poisson structure and Hamiltonian. Following earlier work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible to alleviate in a ...

The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important rôle in the construction of generalisations of the Kerr metric, and in the uncovering of hidden symmetries associated with the existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi and Klein-Gordon eq...

We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finitevolume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinh-Gordon equation arise in this case as a zero-curvature condition for a class of multivalued connections on the punctured Riemann sphere, sim...

Klein/Sine-Gordon equations are very important in that they can accurately model many essential physical phenomena. In this paper, we propose a new spectral method using Legendre wavelets as basis for numerical solution of Klein\Sine-Gordon Equations. Due to the good properties of wavelets basis, the proposed method can obtain good spatial and spectral resolution. Moreover, the presented method...

We introduce a new type of splitting method for semilinear partial differential equations. The method is analyzed in detail for the case of the two-dimensional static sine-Gordon equation describing a large area Josephson junction with overlap current feed and external magnetic field. The solution is separated into an explicit term that satisfies the one-dimensional sine-Gordon equation in the ...