Related papers: The principle of superposition for waves
Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudo-differential equation, involving a periodic…
The results of direct numerical simulation of plane-symmetric turbulence of water waves for potential flows within the framework of conformal variables taking into account low-frequency pumping and high-frequency viscous dissipation are…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the…
We propose a simple, intuitive alternative method of deriving the rule for connecting asymptotic wave function amplitudes to scattering probabilities. This is illustrated using the standard example of a 1-D particle reflecting or…
Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been…
We present a variational wavefunction which explains the behaviour of the supersolid state formed by hard-core bosons on the triangular lattice. The wavefunction is a linear superposition of {\em only and all} configurations minimising the…
This paper is devoted to study the asymptotic stability of wave equations with constant coefficients coupled by velocities. By using Riesz basis approach, multiplier method and frequency domain approach respectively, we find the sufficient…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
We consider the problem of approximating a function using Herglotz wave functions, which are a superposition of plane waves. When the discrepancy is measured in a ball, we show that the problem can essentially be solved by considering the…
One-dimensional optical waveguiding is revisited using the electromagnetic deduction of Fresnel formulas relating the incident, reflected, and transmitted waves on the abrupt interface between two different optical media. Throughout the…
The frozen Gaussian approximation provides a highly efficient computational method for high frequency wave propagation. The derivation of the method is based on asymptotic analysis. In this paper, for general linear strictly hyperbolic…
High-order wave-making theories are becoming available but are limited to certain ranges of waves and wavemaker types in their applicability. Alternatively, machine learning can be considered to find nonlinear functional relationships.…
We present three different methods of calculating the non-relativistic dynamics of a quantum matter-wave evolving in a superposition of the inertial and accelerated motions. The relative phase between the two, which is classically…
Cumulation of shock snd detonation waves was considered. Computations were carried out by use of second-order central-difference scheme. Cumulation of waves in cone region with scales of 1 meter was studied. Pictures of flow in shock and…
The generation of second and third harmonics by an acoustic wave propagating along one dimension in a weakly nonlinear elastic medium that is loaded harmonically in time with frequency $\omega_0$ at a single point in space, is analyzed by…
The multiplicative (or geometric) calculus is a non-Newtonian calculus derived from an arithmetic in which the operations of addition/subtraction/multiplication are replaced by multiplication/division/exponentiation. A major difference…
Generalized Plane Waves (GPWs) were introduced to take advantage of Trefftz methods for problems modeled by variable coefficient equations. Despite the fact that GPWs do not satisfy the Trefftz property, i.e. they are not exact solutions to…
An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a…
Here to represent the propagation of waves I attempted to describe them separately in space and time domains. The time and space wave equations are obtained and investigated, and formulas for the wave propagation are expressed. I also tried…