Light quanta and heavy bosons

1960 ◽  
Vol 257 (1290) ◽  
pp. 283-290 ◽  
Keyword(s):  
Wave Equation ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Light Quantum ◽  
Zero Mass ◽  
Light Quanta ◽  
Spin Triplet ◽  
Spin Properties ◽  
K Mesons ◽  
New Treatment

The new treatment of space-time reflexions presented in a recent paper has led to wave equations whose solutions describe π- and K-mesons with correct isobaric spin properties. Generalization of this wave equation now leads to (i) an isobaric spin triplet (π-mesons), (ii) a singlet with zero mass (Maxwell equations, light quantum), (iii) an isobaric spin quadruplet with zero mechanical spin (K-mesons), and (iv) a particle with equal isobaric spin properties, but unit mechanical spin.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

On the existence of compressional MHD oscillations in an inhomogeneous magnetoplasma

1990 ◽  
Vol 44 (2) ◽  
pp. 361-375 ◽  
Author(s):  
Andrew N. Wright
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Density Distribution ◽  
Cold Plasma ◽  
Wave Equations ◽  
Perturbation Field ◽  
Plasma Density Distribution ◽  
Background Magnetic Field ◽  
Transverse Fields ◽  
The Magnetic Field

In a cold plasma the wave equation for solely compressional magnetic field perturbations appears to decouple in any surface orthogonal to the background magnetic field. However, the compressional fields in any two of these surfaces are related to each other by the condition that the perturbation field b be divergence-free. Hence the wave equations in these surfaces are not truly decoupled from one another. If the two solutions happen to be ‘matched’ (i.e. V.b = 0) then the medium may execute a solely compressional oscillation. If the two solutions are unmatched then transverse fields must evolve. We consider two classes of compressional solutions and derive a set of criteria for when the medium will be able to support pure compressional field oscillations. These criteria relate to the geometry of the magnetic field and the plasma density distribution. We present the conditions in such a manner that it is easy to see if a given magnetoplasma is able to executive either of the compressional solutions we investigate.

scholarly journals Some arguments for the wave equation in Quantum theory

2021 ◽  
Vol 5 (1) ◽  
pp. 314-336
Author(s):  
Tristram de Piro ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Continuity Equation ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Atomic System ◽  
Balmer Series ◽  
Inertial Frames ◽  
The Stability

We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.

THE WAVE EQUATIONS FOR THE WEYL TENSOR/SPINOR AND DIMENSIONALLY DEPENDENT TENSOR IDENTITIES

1996 ◽  
Vol 05 (03) ◽  
pp. 217-225 ◽  
Author(s):  
FREDRIK ANDERSSON ◽  
S. BRIAN EDGAR
Keyword(s):  
Wave Equation ◽  
Large Class ◽  
Weyl Tensor ◽  
Wave Equations ◽  
Dimensional Case ◽  
Weyl Spinor ◽  
Four Dimensions ◽  
Identity Matching ◽  
Tensor Identity ◽  
First Time

By reconciling the wave equation for the Weyl tensor with the corresponding wave equation for the Weyl spinor, we establish a new tensor identity—involving the sum of terms each consisting of a product of the Weyl and Ricci tensors—valid in four (and only four) dimensions. This enables us to give, for the first time, the correct and simplest form of the wave equation for the Weyl tensor in four-dimensional nonvacuum spacetimes. The wave equation for the Weyl tensor in n(> 4) dimensional nonvacuum spaces is also presented for the first time; we show that there does not exist an analogous n-dimensional tensor identity matching the four-dimensional one, and so it follows that there does not exist an analogous simplification of the Weyl wave equation in the n-dimensional case. It is also shown how our new identity, and some other recently discovered identities, relate to a large class of dimensionally dependent identities found some time ago by Lovelock.

Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians

2021 ◽  
Vol 273 (1339) ◽  
Author(s):  
Gong Chen
Keyword(s):  
Wave Equation ◽  
Charge Transfer ◽  
Wave Equations ◽  
Linear Models ◽  
Energy Estimate ◽  
Strichartz Estimates ◽  
Content Type ◽  
Scattering States ◽  
Scattering State ◽  
A Charge

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R 3 \mathbb {R}^{3} : \[ ∂ t t u − Δ u + ∑ j = 1 m V j ( x − v → j t ) u = 0. \partial _{tt}u-\Delta u+\sum _{j=1}^{m}V_{j}\left (x-\vec {v}_{j}t\right )u=0. \] The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [Comm. Math. Phys. 364 (2018), no. 1, pp. 45–82].

scholarly journals On the Fractional Wave Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 874
Author(s):  
Francesco Iafrate ◽  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Wave Equations ◽  
Stable Process ◽  
Space Time ◽  
Probabilistic Interpretation ◽  
Symmetric Stable Process ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation

In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d−dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

scholarly journals Time-dependent attractor of wave equations with nonlinear damping and linear memory

2019 ◽  
Vol 17 (1) ◽  
pp. 89-103
Author(s):  
Qiaozhen Ma ◽  
Jing Wang ◽  
Tingting Liu
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Time Dependent ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

Abstract In this article, we consider the long-time behavior of solutions for the wave equation with nonlinear damping and linear memory. Within the theory of process on time-dependent spaces, we verify the process is asymptotically compact by using the contractive functions method, and then obtain the existence of the time-dependent attractor in $\begin{array}{} H^{1}_0({\it\Omega})\times L^{2}({\it\Omega})\times L^{2}_{\mu}(\mathbb{R}^{+};H^{1}_0({\it\Omega})) \end{array}$.

Global well-posedness and self-similarity for semilinear wave equations in a time-weighted framework of Besov type

2020 ◽  
Vol 17 (01) ◽  
pp. 123-139
Author(s):  
Lucas C. F. Ferreira ◽  
Jhean E. Pérez-López
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Besov Spaces ◽  
Wave Equations ◽  
Well Posedness ◽  
Self Similarity ◽  
Semilinear Wave Equations ◽  
Semilinear Wave Equation

We show global-in-time well-posedness and self-similarity for the semilinear wave equation with nonlinearity [Formula: see text] in a time-weighted framework based on the larger family of homogeneous Besov spaces [Formula: see text] for [Formula: see text]. As a consequence, in some cases of the power [Formula: see text], we cover a initial-data class larger than in some previous results. Our approach relies on dispersive-type estimates and a suitable [Formula: see text]-product estimate in Besov spaces.

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