scholarly journals Several localized waves induced by linear interference between a nonlinear plane wave and bright solitons

2018 ◽  
Vol 28 (1) ◽  
pp. 013111 ◽  
Author(s):  
Yan-Hong Qin ◽  
Li-Chen Zhao ◽  
Zhan-Ying Yang ◽  
Wen-Li Yang
Keyword(s):  
Plane Wave ◽  
Bright Solitons ◽  
Nonlinear Plane ◽  
Localized Waves

scholarly journals Exact Solutions Superimposed with Nonlinear Plane Waves

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
B. S. Desale ◽  
Vivek Sharma
Keyword(s):  
Exact Solution ◽  
Plane Wave ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Large Scale ◽  
Plane Waves ◽  
Boussinesq Equations ◽  
Integral Curves ◽  
Nonlinear Plane ◽  
Scale Motion

The flow of fluid in atmosphere and ocean is governed by rotating stratified Boussinesq equations. Through the literature, we found that many researchers are trying to find the solutions of rotating stratified Boussinesq equations. In this paper, we have obtained special exact solutions and nonlinear plane waves. Finally, we provide exact solutions to rotating stratified Boussinesq equations with large scale motion superimposed with the nonlinear plane waves. In support of our investigations, we provided two examples: one described the special exact solution and in second example, we have determined the special exact solution superimposed with nonlinear plane wave. Also, we depicted some integral curves that represent the flow of an incompressible fluid particle on the planex1+x2=L(constant)as the particular case.

MODULATIONAL INSTABILITY IN NONLINEAR BI-INDUCTANCE TRANSMISSION LINE

2005 ◽  
Vol 19 (26) ◽  
pp. 3961-3983 ◽  
Author(s):  
E. KENGNE ◽  
KUM K. CLETUS
Keyword(s):  
Plane Wave ◽  
Transmission Line ◽  
Traveling Waves ◽  
Modulational Instability ◽  
Ginzburg Landau ◽  
Complex Demodulation ◽  
Wave Solutions ◽  
Ginzburg Landau Equations ◽  
Nonlinear Plane ◽  
The Right

A nonlinear dissipative transmission line is considered and by performing the complex demodulation technique of the signal which allows, in particularly, to separate the right traveling and left traveling waves, we show that the amplitudes of these waves can be described by a complex coupled Ginzburg–Landau equations (CG-LE). The so-called phase winding solutions of the constructed CG-LE is analyzed. We also study the coherent structures in the obtained complex Ginzburg–Landau system. We show that the constructed CG-LE possesses nonlinear plane wave solutions and the modulational instability of these solutions is analyzed. The condition of the modulational instability is given in term of the coefficients of the constructed CG-LE and then in term of the wavenumber of the two right traveling and left traveling waves in the considered transmission line. The results obtained here show that the nonlinear plane wave solutions of the CG-LE under perturbation with zero wavenumber cannot be stable under modulation.

A NONLINEAR PLANE-WAVE ALGORITHM FOR DIFFRACTIVE PROPAGATION INVOLVING SHOCKWAVES

1993 ◽  
Vol 01 (03) ◽  
pp. 371-393 ◽  
Author(s):  
P. TED CHRISTOPHER
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Frequency Domain ◽  
Time Domain ◽  
Burgers Equation ◽  
Propagation Model ◽  
Nonlinear Beam ◽  
Nonlinear Plane ◽  
Very High ◽  
Plane Wave Propagation

A new algorithm for nonlinear plane-wave propagation is presented. The algorithm uses a novel time domain representation to account for nonlinearity, while accounting for absorption in the frequency domain. The new algorithm allows for accurate representations of diffractive shockwave propagation in the framework of an existing nonlinear beam propagation model using far fewer harmonics (and thus time) than alternative algorithms based on a frequency domain solution to Burgers' equation. The new algorithm is tested against the frequency domain solution to Burgers' equation in a variety of cases and then used to model a focused ultrasonic piston transducer operating at very high source intensities.

NONLINEAR PLANE WAVES IN A LONG-WAVELENGTH CONVECTION MODEL

2001 ◽  
Vol 11 (11) ◽  
pp. 2867-2874
Author(s):  
A. M. MANCHO ◽  
L. VÁZQUEZ ◽  
H. HERRERO ◽  
S. HOYAS
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Plane Wave ◽  
Prandtl Number ◽  
Plane Waves ◽  
Long Wavelength ◽  
Wave Solutions ◽  
Convection Model ◽  
Nonlinear Plane

The partial differential equation (PDE) associated with the long-wavelength regime that describes convection between rigid and poorly conducting boundaries in an infinite Prandtl number fluid is studied in this document. This PDE is reduced to a set of ordinary differential equations (ODE) by looking for the exact nonlinear plane wave solutions. Solving this ODE several kinds of oscillatory attractors are obtained. These attractors are compared to oscillations observed in experiments on fluids and some features are also recovered.

Nonlinear plane wave solutions in the semiclassic Maxwell-Bloch laser equations

1993 ◽  
Vol 66 (3-4) ◽  
pp. 412-426 ◽  
Author(s):  
I. Pastor ◽  
V.M. Pérez García ◽  
F. Encinas Sanz ◽  
J.M. Guerra ◽  
L. Vázquez
Keyword(s):  
Plane Wave ◽  
Wave Solutions ◽  
Nonlinear Plane

scholarly journals X-ray third-order nonlinear plane-wave Bragg-case dynamical diffraction effects in a perfect crystal. Erratum

2016 ◽  
Vol 23 (5) ◽  
pp. 1272-1272
Author(s):  
Minas K. Balyan
Keyword(s):  
Plane Wave ◽  
Perfect Crystal ◽  
Third Order ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Nonlinear Plane ◽  
Diffraction Effects

Formulae in the paper by Balyan (2015) [J. Synchrotron Rad.22, 1410–1418] are corrected.

scholarly journals Persistent gravitational wave observables: Nonlinear plane wave spacetimes

2020 ◽  
Vol 101 (10) ◽  
Author(s):  
Éanna É. Flanagan ◽  
Alexander M. Grant ◽  
Abraham I. Harte ◽  
David A. Nichols
Keyword(s):  
Plane Wave ◽  
Gravitational Wave ◽  
Nonlinear Plane

Visualizing the Tumor Microvasculature With a Nonlinear Plane-Wave Doppler Imaging Scheme Based on Amplitude Modulation

2016 ◽  
Vol 35 (2) ◽  
pp. 699-709 ◽  
Author(s):  
Charles Tremblay-Darveau ◽  
Ross Williams ◽  
Laurent Milot ◽  
Matthew Bruce ◽  
Peter N. Burns
Keyword(s):  
Plane Wave ◽  
Amplitude Modulation ◽  
Doppler Imaging ◽  
Tumor Microvasculature ◽  
Nonlinear Plane

Theory and Errors in Stereo Electron Microscopy

1968 ◽  
Vol 26 ◽  
pp. 336-337
Author(s):  
J. M. Pankratz
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Plane Wave ◽  
Focal Length ◽  
Foil Thickness ◽  
Points Of Interest ◽  
Transmission Electron ◽  
Vertical Spacing ◽  
Illuminating System

It is often desirable in transmission electron microscopy to know the vertical spacing of points of interest within a specimen. However, in order to measure a stereo effect, one must have two pictures of the same area taken from different angles, and one must have also a formula for converting measured differences between corresponding points (parallax) into a height differential.Assume (a) that the impinging beam of electrons can be considered as a plane wave and (b) that the magnification is the same at the top and bottom of the specimen. The first assumption is good when the illuminating system is overfocused. The second assumption (the so-called “perspective error”) is good when the focal length is large (3 x 107Å) in relation to foil thickness (∼103 Å).

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