Related papers: Non-linear effects for cylindrical gravitational t…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries…
This article is an extended version of a presentation given at KOZWaves 2024: The 6th Australasian Conference on Wave Science, held in Dunedin, New Zealand. Soliton methods were initially introduced to study equations such as the…
We present a simple and constructive method to find $N$-soliton solutions of the equation suggested by Davydova and Lashkin to describe the dynamics of nonlinear ion-cyclotron waves in a plasma and subsequently known (in a more general form…
Contrary to the common understanding, the Sine-Gordon equation in (1+2) dimensions does have N-soliton solutions for any N. The Hirota algorithm allows for the construction of static N-soliton solutions (i.e., solutions that do not depend…
We present an exact plane wave solution of the most general shift-symmetric Horndeski (generalized Galileon) theory. The solution consists of the scalar part, and the gravitational part with two polarization modes. The former is due to the…
We discuss the effects of an isolated gravitational lens on the rotation of the plane of polarization of linearly polarized light rays, the so called gravitational Faraday rotation, in metric theories of gravity. By applying the thin lens…
We theoretically investigate the properties of phonon-polariton inhomogeneous harmonic wave, cnoidal wave and spatial soliton propagating in boundless dielectric medium and compute the shape of nonlinear vector polariton wave. We obtain…
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $\xi^{v}$ and $\xi^{u}$ of the separation vector behave as…
We analyze the structure of the vacuum polarization tensor in the presence of a background electromagnetic field in a medium. We use various discrete symmetries and crossing symmetry to constrain the form factors obtained for the most…
We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture…
Interaction of a solitary wave with a long background wave is studied within the framework of rotation modified Benjamin-Ono equation describing internal waves in a deep fluid. With the help of asymptotic method, we find stationary and…
We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the…
Alternative theories of gravity not only modify the polarization contents of the gravitational wave, but also affect the motions of the stars and the energy radiated away via the gravitational radiation. These aspects leave imprints in the…
We show that the relativistic effects are negligibly small in the non-linear density and velocity bispectra. Although the non-linearities of Einstein equation introduce additional non-linear terms to the Newtonian fluid equations, the…
The optical Faraday effect describes the rotation of linear polarization upon propagation through a medium in the presence of a longitudinal magnetic field. The effect arises from a different phase delay between the right and left handed…
Gravitational radiation can be expressed in terms of an infinite series of radiative, symmetric trace-free (STF) multipole moments which can be connected to the behavior of the source. We consider a truncated model for gravitational…
With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of…
The conversion of gravitational to electromagnetic waves in the presence of background magnetic fields is known as the inverse Gertsenshtein effect, analogous to the Primakoff effect for axions. Rephrasing this conversion as a classical…
We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing…