scholarly journals On the Wave Equation for Spin 1 in Hamiltonian Form

1955 ◽  
Vol 14 (2) ◽  
pp. 166-167
Author(s):  
Izuru Fujiwara
Keyword(s):  
Wave Equation ◽  
Hamiltonian Form

Wave Equation for Spin 0 in Hamiltonian Form

1955 ◽  
Vol 99 (5) ◽  
pp. 1572-1573 ◽  
Author(s):  
K. M. Case
Keyword(s):  
Wave Equation ◽  
Hamiltonian Form

The wave equation for spin 1 in Hamiltonian form

1955 ◽  
Vol 229 (1176) ◽  
pp. 39-43 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Differential Equations ◽  
Matrix Equation ◽  
Hamiltonian Form ◽  
Initial Value ◽  
Potential Vector ◽  
Spin Number ◽  
Proca Equations ◽  
Derivatives Of

If from the differential equations that hold in a Proca field you select the ten that express the time derivatives of the ten components involved, i. e. of the ‘electromagnetic’ field and its potential vector, you obtain right away for the ten-componental entity an equation that may be said to be at the same time of the Schrödinger, the Dirac and the Kemmer type. The four 10 x 10-matrices that occur as coefficients are Hermitian and satisfy Kemmer’s commutation rules. The fifth is easily constructed. Those of the Proca equations that were not included are merely injunctions on the initial value. They are expressed by one matrix equation, that makes it evident that, once posited, they are preserved. The three spin matrices are indicated. The spin number is 1 or 0, but the aforesaid injunctions exclude 0.

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. 

DeWitt geometry and the wave equation in hyper-volume

2020 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Equation

DeWitt geometry and the wave equation in hyper-volume

Classical and generalized of a mixed problem– solutions for a non-homogeneous wave equation

2019 ◽  
Vol 484 (1) ◽  
pp. 18-20
Author(s):  
A. P. Khromov ◽  
V. V. Kornev
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Mixed Problem ◽  
Homogeneous Equation ◽  
Generalized Solution ◽  
Problem Solution ◽  
Homogeneous Wave ◽  
Homogeneous Wave Equation ◽  
Explicit Expressions

This study follows A.N. Krylov’s recommendations on accelerating the convergence of the Fourier series, to obtain explicit expressions of the classical mixed problem–solution for a non-homogeneous equation and explicit expressions of the generalized solution in the case of arbitrary summable functions q(x), ϕ(x), y(x), f(x, t).

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