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The behavior of sufficiently regular solutions to semilinear hyperbolic equations has attracted a great deal of attention in the past decades, concerning local/global existence, finite time blow-up, critical exponents, and propagation of…
It will be shown that a given realization of nonlinear electrodynamics, used as source of Einstein's equations, generates a cosmological model with interesting features, namely a phase of current cosmic acceleration, and the absence of an…
In modern physics only relative quantities are considered to have physical significance. For example, position assigned to a system depends on the choice of coordinates, and only relative distances between different systems have physical…
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for…
By associating a binary signal with the relativistic worldline of a particle, a binary form of the phase of non-relativistic wavefunctions is naturally produced by time dilation. An analog of superposition also appears as a Lorentz…
It is shown that the addition of a non-linear term to the Lagrangian of the electromagnetic field yields a fluid with an asymptotically super-negative equation of state, causing an accelerated expansion of the universe. Some general…
Nonlinear quantum mechanics at the Planck scale can produce nonlocal effects contributing to resolution of singularities, to cosmic acceleration, and modified black-hole dynamics, while avoiding the usual causality issues.
Here we prove a global existence theorem for the solutions of the semi-linear wave equation with critical non-linearity admitting a positive definite Hamiltonian. Formulating a parametrix for the wave equation in a globally hyperbolic…
This paper belongs to a group of work in the intersection of symbolic computation and group analysis aiming for the symbolic analysis of differential equations. The goal is to extract important properties without finding the explicit…
The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. An…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
The perturbation theory plays an important role in studying structure formation in cosmology and post-Newtonian physics, but not all phenomena can be described by the linear perturbation theory. Thus, It is necessary to study exact…
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…
We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…
We show that Einstein equations are compatible with the presence of massive point particle idealization and find the corresponding two parameter family of solutions. They are complete defined by the bare mechanical mass $M>0$ and the…
We derive an analytic expression for the two-point correlation function in redshift space which (i) is nonlinear; (ii) is valid on the full sky, i.e. the distant-observer limit is not assumed; (iii) can account for the effect of…
A superposition rule is a particular type of map that enables one to express the general solution of certain systems of first-order ordinary differential equations, the so-called Lie systems, out of generic families of particular solutions…
We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…
Observing a linear superposition principle, a family of new minimal hypersurfaces in Euclidean space is found, as well as that linear combinations of generalized helicoids induce new algebraic minimal cones of arbitrarily high degree.