Consider a standing wave in a stretched string. As we proceed horizontally along the string, the vertical displacement (or amplitude) of the wave increases in one direction, passes through a maximum, decreases to zero and then increases in the opposite direction. The places where the amplitude is zero are called nodes. The nodes lie on a plane called the nodal plane (which lies perpendicular to...

in this paper, lagrangian and equations describing one-dimensional anisotropic non-heisenberg model are studied. in this study we used the generalized coherent states in real parametrizations and the feynman path integral for these states in su(3) group. these equations describe nonlinear dynamics of non-heisenberg ferromagnetic chain completely. solutions of these equations are magnetic solito...

In the first part of this article (after a sketchy theoretical introduction) the various experimental sectors of physics in which Superluminal motions seem to appear are briefly mentioned. In particular, a bird’s-eye view is presented of the experiments with evanescent waves (and/or tunneling photons), and with the “localized Superluminal solutions” (SLS) to the wave equation, like the so-calle...

Maxwell’s equations represent a culmination of classical mathematical physics by offering a compact mathematical formulation of all of electromagnetics including the propagation of light and radiation, as electromagnetic waves. But like in a Greek tragedy, the success of Maxwell’s equations prepared for the collapse of classical mathematical physics and the rise of modern physics based on a con...

where := −∂2 t +∆ and u[0] := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F (u,Du), where D := (∂t,∇)). The goal is to use energy methods to prove local well-posedness for quasilinear equations with data (f, g) ∈ Hs × Hs−1 for large enough s, and then to derive Strichartz esti...

We survey existence and regularity results for semi-linear wave equations. In particular, we review the recent regularity results for the u5-Klein Gordon equation by Grillakis and this author and give a self-contained, slightly simplified proof.

2.1.1 Full Maxwell’s Equations The full set of Maxwell’s equations come in two forms. The first form is called either the integral or volume form and is shown in Table 2.1. These set of four equations show the interrelationships of the basic physical quantities studied in electromagnetics, which are summarized in Table 2.2. This form of Maxwell’s equations elegantly relates volumeand area-integ...

By using an extended ( ′ G )-expansion method, we construct the traveling wave solutions of the (2+1)dimensional Painleve integrable Burgers equations, the (2+1)-dimensional Nizhnik-Novikov-Veselov equations, the (2+1)-dimensional Boiti-Leon-Pempinelli equations and the (2+1)-dimensional dispersive long wave equations, where G satisfies the second order linear ordinary differential equation. By...