Related papers: Derivation of the wave equation
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
The mechanics of wave motion in a medium are founded in conservation laws for the physical quantities that the waves carry, combined with the constitutive laws of the medium, and define Lorentzian structures only in degenerate cases of the…
We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding…
An explanation of polarization entanglement is presented using Maxwells classical electromagnetic theory.Two key features are required to understand these classical origins.The first is that all waves diffract and weakly diffracting…
We consider propagation of high-frequency wave packets along a smooth evolving background flow whose evolution is described by a simple-wave type of solutions of hydrodynamic equations. In geometrical optics approximation, the motion of the…
The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients…
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the…
The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…
A laminar flow of a thin layer of mud down an inclined plane under the action of gravity is considered. The instability of a film flow and the formation of finite amplitude waves are studied in the framework of both two-dimensional…
The standard quantum mechanics assumes Schr\"odinger equation for regular evolution and wave function collapse for measurement. As shown in this paper, only particular collapse equation can continuously transition to Schr\"odinge equation.…
A systematic and full description of the theory for a dissipation mechanism of wind wave energy in a spectral representation is given. As a basis of the theory, the fundamental is stated that the most general dissipation mechanism for wind…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
This paper focus on the theoretical analysis and simulation of electromagnetic wave transforms, which is widely encountered in teaching physics. When the electromagnetic wave is not consistent with the shape of the object, it is often…
While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines the solution of Newton's…
Gravitational waves propagate at the speed of light in general relativity, because of its special relativistic basis. However, light propagation is linked to the electromagnetic phenomena, with the permittivity and permeability constants as…
We consider some of the methods that can be used to reveal the general features of how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical…
Two essential shortcomings of the axiomatics of wave mechanics are revealed, which make its consistent interpretation impossible. The first is that the standard formulation of the superposition principle contradicts the exact solutions of…
Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution…
We explain the collapse of the wavefunction with the notion that, in a measurement, the system observed nucleates a first order phase transition in the measuring device. The possible final states differ by the values of macroscopic…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…