Excitation of nonlinear periodic standing waves in compressible media

2015 ◽  
Vol 50 (6) ◽  
pp. 789-792 ◽  
Author(s):  
A. G. Petrov
Keyword(s):  
Standing Waves ◽  
Periodic Standing Waves

The Low Dimensionality of Time-Periodic Standing Waves in Water of Finite and Infinite Depth

2012 ◽  
Vol 11 (3) ◽  
pp. 1033-1061 ◽  
Author(s):  
Matthew O. Williams ◽  
Eli Shlizerman ◽  
Jon Wilkening ◽  
J. Nathan Kutz
Keyword(s):  
Standing Waves ◽  
Infinite Depth ◽  
Low Dimensionality ◽  
Periodic Standing Waves ◽  
Time Periodic

Highly nonlinear standing water waves with small capillary effect

1998 ◽  
Vol 369 ◽  
pp. 253-272 ◽  
Author(s):  
WILLIAM W. SCHULTZ ◽  
JEAN-MARC VANDEN-BROECK ◽  
LEI JIANG ◽  
MARC PERLIN
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Standing Waves ◽  
High Amplitude ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Ripple Formation ◽  
Node Distribution ◽  
Highly Nonlinear ◽  
Periodic Standing Waves

We calculate spatially and temporally periodic standing waves using a spectral boundary integral method combined with Newton iteration. When surface tension is neglected, the non-monotonic behaviour of global wave properties agrees with previous computations by Mercer & Roberts (1992). New accurate results near the limiting form of gravity waves are obtained by using a non-uniform node distribution. It is shown that the crest angle is smaller than 90° at the largest calculated crest curvature. When a small amount of surface tension is included, the crest form is changed significantly. It is necessary to include surface tension to numerically reproduce the steep standing waves in Taylor's (1953) experiments. Faraday-wave experiments in a large-aspect-ratio rectangular container agree with our computations. This is the first time such high-amplitude, periodic waves appear to have been observed in laboratory conditions. Ripple formation and temporal symmetry breaking in the experiments are discussed.

Water waves in a deep square basin

1995 ◽  
Vol 302 ◽  
pp. 65-90 ◽  
Author(s):  
Peter J. Bryant ◽  
Michael Stiassnie
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Three Dimensional ◽  
Standing Waves ◽  
Two Dimensional ◽  
Initial State ◽  
Dimensional Properties ◽  
Periodic Standing Waves ◽  
The Waves ◽  
Small Disturbances

The form and evolution of three-dimensional standing waves in deep water are calculated analytically from Zakharov's equation and computationally from the full nonlinear bounddary value problem. The water is contained in a basin with a square cross-cection, when three-dimensional properties to pairs of sides are the same. It is found that non-periodic standing waves commonly follow forms of cyclic recurrence over times. The two-dimensional Stokes type of periodic standing waves (dominated by the fundamental harmonic) are shown to be unstable to three dimensional disturbances, but over long times the waves return cyclically close to their initial state. In contrast, the three-dimensional Stokes type of periodic standing waves are found to be stabel to small disturbances. New two-dimensional periodic standing waves with amplitude maxima at other than the fundamental harmonic have been investigated recently (Bryant & Stiassnie 1994). The equivalent three-dimensional standing waves are described here. The new two-dimensional periodic standing waves, like the two-dimensional Stokes standing waves, are found to be unstable to three-dimensional disturbances, and to exhibit cyclic recurrence over long times. Only some of the new three-dimensional periodic standing waves are found to be stable to small disturbances.

scholarly journals Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber

2019 ◽  
Vol 53 (1) ◽  
pp. 87-107
Author(s):  
Felipe Alexander Pipicano ◽  
Juan Carlos Muñoz Grajales
Keyword(s):  
Hamiltonian System ◽  
Optical Fiber ◽  
Numerical Simulations ◽  
Standing Wave ◽  
Kerr Effect ◽  
Wave Equations ◽  
Pulse Propagation ◽  
Standing Waves ◽  
Wave Solutions ◽  
Periodic Standing Waves

We establish existence of periodic standing waves for a model to describe the propagation of a light pulse inside an optical fiber taking into account the Kerr effect. To this end, we apply the Lyapunov Center Theorem taking advantage that the corresponding standing wave equations can be rewritten as a Hamiltonian system. Furthermore, some of these solutions are approximated by using a Newton-type iteration, combined with a collocation-spectral strategy to discretize the system of standing wave equations. Our numerical simulations are found to be in accordance with our analytical results.

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