This article is an introduction to wave equations, emphasizing for simplicity the case of a single space dimension. What we mean by a wave equation will gradually be made more precise as we proceed, but at first, we will just a mean a certain kind of ordinary differential equation on the space C∞(Rn, V ), where V is some finite dimensional vector space, usually R or C, (and generally we will ta...

The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector φ1 of ...

Recently, vector soliton equations (or coupled soliton equations) such as the vector Nonlinear Schrödinger (vNLS) equation have received so much attention in mathematical physics and nonlinear physics. Especially, the vNLS equation has been studied by several researchers from both mathematical and physical points of view [1-5]. It was pointed out that vector solitons can be used in the construc...

Waveform patterns of P, ST and T vector functions of Frank-lead rest and exercise vectorcardiograms (VCG) of 375 ostensibly normal males, aged 50-70 years, were evaluated by waveform vector analysis (WVA). This procedure suitably quantified waveform information, providing a stable reduced data base comprising mean vector (MV), gradient vector (GV), convex vector (CV), sigmoid vector (SV), and q...

Recently, vector soliton equations (or coupled soliton equations) such as the vector Nonlinear Schrödinger (vNLS) equation have received so much attention in mathematical physics and nonlinear physics. Especially, the vNLS equation has been studied by several researchers from both mathematical and physical points of view [1-5]. It was pointed out that vector solitons can be used in the construc...

This article introduces the abstract notion of finite wave packet groups over finite fields as the finite group of dilations, translations, and modulations. Then it presents a unified theoretical linear algebra approach to the theory of wave packet transforms (WPT) over finite fields. It is shown that each vector defined over a finite field can be represented as a finite coherent sum of wave pa...

Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates. PACS: 24.10.Jv, 21.60.Cs, 24.80.+y, 21.10.-k *E-mail address: [email protected] †E...

In a recent few years, the further heating of the magnetically confined plasmas to thermonuclear temperature by using a high power source with a frequency w/2n near the lower hybrid frequency, has been investigated with great interests. For the launched wave to penetrate through the plasma boundary without significant reflection, it is desired that the parallel phase velocity of the wave, w/kz ...

The Darboux-dressing transformations are applied to the Lax pair associated with systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both ‘bright’ and ‘dark’ soliton solutions. The general formalism is set up and the relevant equations are explicitly solved. Several instances of multicomponent wave equations of applicative interest, such as vector...