Related papers: Some global aspects of linear wave equations
The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…
We make some remarks on the linear wave equation concerning the existence and uniqueness of weak solutions, satisfaction of the energy equation, growth properties of solutions, the passage from bounded to unbounded domains, and…
These are the very unpretentious lecture notes for the minicourse "Introduction to evolution equations in Geometry," a part of the Brazilian Colloquium of Mathematics held at IMPA, in July of 2009.
The goal of this short report is to summarise some key results based on our previous works on model independent tests of gravity at large scales in the Universe, their connection with the properties of gravitational waves, and the…
We continue here with previous investigations on the global behavior of general type non-linear wave equations for a class of small, scale-invariant initial data. The method is based on the use of a new set of Strichartz estimates for the…
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow…
This is a tutorial for the many-worlds theory by Everett, which includes some of my personal views. It has two main parts.The first main part shows the emergence of many worlds in a universe consisting of only a Mach-Zehnder interferometer.…
We apply Laplace's tidal theory to the evolution of lunar and solar tides on the geologic timescale of Earth's rotation and focus on the tidal resonance. We study the global tide in the mid-ocean far away from continents. On the short…
In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…
Introductory calculus-based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
We review the state of the field of gravitational wave astrophysics, framing the challenges, current observations, and future prospects within the context of the predictions of Einstein's theory of general relativity.
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo…
We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert problem approach is used to recast the governing equations…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations…
In this paper, we use the equivariant degree theory to establish a global bifurcation result for the existence of non-stationary branches of solutions to a nonlinear, two-parameter family of hyperbolic wave equations with local delay and…
A combination of some weighted energy estimates is applied for the Cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions. Alternative proofs for global solutions are shown including the…
Many new models of wave turbulence -- frozen, mesoscopic, laminated, decaying, sand-pile, etc. -- have been developed in the last decade aiming to solve problems seemingly not solvable in the framework of the existing wave turbulence theory…
These lectures are envisioned to be an introductory, basic course in gravitational-wave physics.