Related papers: Non-Diffracting Waves: A new introduction
The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new approach to direct numerical simulation of solutions to…
By a generalized bidirectional decomposition method, we obtain many new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; various of them…
In the present study, the authors introduce a geometrically improved model inspired by the mammalian basilar membrane's properties and special vibratory behavior while conducting a parametric investigation. The goal of this model is to…
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…
Gravitational wave (GW) astronomy offers the potential to probe the wave-optics regime of gravitational lensing. Wave optics (WO) effects are relevant at low frequencies, when the wavelength is comparable to the characteristic lensing time…
The general form of the cubic Boussinesq-type equation is considered. In special cases, this equation is reduced to the three different versions of the cubic Boussinesq equations and also the generalized modified cubic Boussinesq equation.…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
We have developed a new family of limited-diffraction electromagnetic X-shaped waves based on the scalar "X waves" discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical…
In this chapter, we discuss experiments that realize the discrete nonlinear Schr\"odinger (DNLS) equations. The relevance of such descriptions arises from the competition of three common features: nonlinearity, dispersion, and a medium to…
The Dirichlet problem for the wave equation is a classical example of a problem which is not well-posed. Nevertheless, it has been used to model internal waves oscillating sinusoidally in time, in various situations, standing internal waves…
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…
Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate…
We present exact N-soliton optical pulses riding on a continuous-wave (c.w.) beam that propagate through and interact with a two-level active optical medium. Their representation is derived via an appropriate generalization of the inverse…
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
Fully non-linear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave…