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Traveling Wave Method

Дифференциальные уравнения, 2023
A survey of the development of the traveling wave method for one-dimensional media is presented. The main results and changes in the statement of the problem of representing solutions of linear systems of partial differential equations in terms of “traveling waves” (more precisely, in terms of a system of wave transport equations) are presented.
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Traveling Waves in Shallow Seas of Variable Depths [PDF]

open access: yesSymmetry, 2022
The problem of the existence of traveling waves in inhomogeneous fluid is very important for enabling an explanation of long-distance wave propagations such as tsunamis and storm waves.
Efim Pelinovsky   +2 more
exaly   +2 more sources

Sinusoidal Traveling Waves

Transactions of the American Institute of Electrical Engineers, 1936
The theory of transients arising from the sudden application of a sinusoidal potential is presented in this paper, for the distortionless transmission line. The solution is given in the form of a series of damped sinusoidal traveling waves, the reflections diminishing progressively until the steady state is reached.
Ernst Weber, Frank E. Kulman
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Traveling Waves [PDF]

open access: yes, 2013
Traveling waves are, mathematically speaking, partial differential equations which can be expresses as U(x-ct), where x is the spatial variable, t is time, and c is the speed of the wave.
Humpherys, Dr. Jeffery, Rudd, Keith
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Travelling Waves for the Brio System

Journal of Nonlinear Science, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Traveling Wave and Multiple Traveling Wave Solutions of Parabolic Equations

SIAM Journal on Mathematical Analysis, 1982
We consider scalar equations $u_t = f(u_{xx} ,u_x ,u)$ with $\frac{\partial }{{\partial \alpha }}f(\alpha ,\beta ,\gamma ) \geq 1$. We first determine the stability of the monotonic traveling wave solutions $u(t,x) = \phi (x - ct,c)$. We then study the continued existence and bifurcations of these solutions as the wavespeed c varies.
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Oscillations and travelling waves

1995
A very important class of shell patterning is caused by pigment productions that occur only during a short time interval, followed by an inactive period without pigment production. Stripes parallel to the growing edge and oblique lines belong to this class of patterns. Oscillations can occur if the antagonist reacts too slowly.
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Travelling Waves

1990
Abstract In the previous chapter we dealt with the existence and spontaneous formation of stable spatially non-uniform patterns. Here, we consider another form of spatial behaviour. We envisage a (long) tube, initially containing a spatially uniform distribution of reactants.
Peter Gray, Stephen K Scott
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Distortion of traveling waves by corona

Electrical Engineering, 1937
In order to make possible the prediction of the attenuation and distortion of lightning waves on transmission lines an equation is proposed that relates the change of shape of a traveling wave to the corona loss on the line at normal operating frequency. Results obtained by computation from this formula are compared with experimental results of various
H. H. Skilling, P. de K. Dykes
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Traveling‐wave dielectrophoresis of microparticles

ELECTROPHORESIS, 1992
AbstractThe traveling‐wave‐induced linear transfer of dielectric particles like living cells and artificial objects of microscopic dimensions is analyzed. It is shown that the electrode geometries must correspond to particle sizes to allow an effective manipulation of particles immersed in weakly electrolytic solutions by high frequency traveling waves.
R, Hagedorn   +3 more
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