Related papers: A Kirchoff-Sobolev parametrix for the wave equatio…
Theoretically, in (1+1) dimensions, one can have Klein-Fock-Gordon-Majorana (KFGM) particles. More precisely, these are one-dimensional (1D) Klein-Fock-Gordon (KFG) and Majorana particles at the same time. In principle, the wave equations…
We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a…
This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such…
We study solutions to the Yang-Mills-Higgs equations on the maximal Cauchy development of the data given on a ball of radius $R$ in $\mathbb{R}^3$. The energy of the data could be infinite and the solution grows at most inverse polynomially…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…
A solution to the 50 year old problem of a spinning particle in curved space has been recently derived using an extension of Clifford calculus in which each geometric element has its own coordinate. This leads us to propose that all the…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphsim from an appropriately defined graph space to L^2. The results rely on well-posedness and stability of the…
The objective of this work is the construction of `Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value…
The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in (3+1) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We…
The variational methods implemented on a quadratic Yang-Mills type Lagrangian yield two sets of equations interpreted as the field equations and the energy-momentum tensor for the gravitational field. A covariant condition is imposed on the…
We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…
In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and…
Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of parametrized or unparametrized curves have several desirable…
The basic principles of generalization of the group theoretical approach to the relativistic wave equations on curved spaces are examined. The general method of the determination of wave equations from the known symmetry group of a…
We refine metrical statements in the style of the Khintchine-Groshev Theorem by requiring certain coprimality constraints on the coordinates of the integer solutions.
We introduce a new class of piece-wise quadratic potentials for nonlinear wave equations with a kink solutions. The potentials allow an exact description of the spectral properties for the linearized equation at the kink. This description…
In this paper, we seek to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. We first present a conditional result on the construction of nontrivial global solutions to a general system of…
In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…