Influence of the peripheral field on the structure of a nonlinear focus arising during the propagation of a wave beam in a medium with cubic nonlinearity

2009 ◽  
Vol 52 (1) ◽  
pp. 57-66
Author(s):  
S. N. Vlasov
Keyword(s):  
Wave Beam ◽  
Cubic Nonlinearity ◽  
Nonlinear Focus

scholarly journals A Compact Dual-Band and Dual-Polarized Millimeter-Wave Beam Scanning Antenna Array for 5G Mobile Terminals

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yuqi He ◽  
Sihan Lv ◽  
Luyu Zhao ◽  
Guan-Long Huang ◽  
Xiaoming Chen ◽  
...  
Keyword(s):  
Antenna Array ◽  
Millimeter Wave ◽  
Wave Beam ◽  
Dual Band ◽  
Mobile Terminals ◽  
Beam Scanning ◽  
Dual Polarized ◽  
Scanning Antenna

scholarly journals Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1398
Author(s):  
Natalia Kolkovska ◽  
Milena Dimova ◽  
Nikolai Kutev
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Second Derivative ◽  
Cubic Nonlinearity ◽  
Abstract Theory ◽  
Power Type ◽  
Analytical Formulas ◽  
Stability Of Solitary Waves ◽  
The Stability ◽  
Double Dispersion

We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity f(u)=a|u|pu+b|u|2pu,p>0,a∈R,b∈R,b≠0. The stability of solitary waves with velocity c, c2<1 is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function d(c), related to some conservation laws. We derive explicit analytical formulas for the function d(c) and its second derivative for quadratic-cubic nonlinearity f(u)=au2+bu3 and parameters b>0, c2∈0,min1,h1h2. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity f(u)=bu3.

scholarly journals Circularly‐polarised end‐fire antenna and arrays for 5G millimetre‐wave beam‐steering systems

2020 ◽  
Vol 14 (9) ◽  
pp. 980-987 ◽  
Author(s):  
Khaled Al‐Amoodi ◽  
Mohammad Mahdi Honari ◽  
Rashid Mirzavand ◽  
Jordan Melzer ◽  
Duncan G. Elliott ◽  
...  
Keyword(s):  
Wave Beam ◽  
Beam Steering ◽  
Millimetre Wave

834  W, 1769  kHz spectral bandwidth, continuous-wave, beam densely folded Innoslab amplifier

2017 ◽  
Vol 42 (6) ◽  
pp. 1109 ◽  
Author(s):  
Jian Ning ◽  
Kezhen Han ◽  
Jingliang He ◽  
Yiran Wang ◽  
Hongkun Nie ◽  
...  
Keyword(s):  
Continuous Wave ◽  
Wave Beam ◽  
Spectral Bandwidth

Transcritical two-layer flow over topography

1987 ◽  
Vol 178 ◽  
pp. 31-52 ◽  
Author(s):  
W. K. Melville ◽  
Karl R. Helfrich
Keyword(s):  
Steady Flow ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Single Layer ◽  
Cubic Nonlinearity ◽  
Arbitrary Length ◽  
Weakly Nonlinear ◽  
Flow Over Topography ◽  
Layer Flow

The evolution of weakly-nonlinear two-layer flow over topography is considered. The governing equations are formulated to consider the effects of quadratic and cubic nonlinearity in the transcritical regime of the internal mode. In the absence of cubic nonlinearity an inhomogeneous Korteweg-de Vries equation describes the interfacial displacement. Numerical solutions of this equation exhibit undular bores or sequences of Boussinesq solitary waves upstream in a transcritical regime. For sufficiently large supercritical Froude numbers, a locally steady flow is attained over the topography. In that regime in which both quadratic and cubic nonlinearity are comparable, the evolution of the interface is described by an inhomogeneous extended Kortewegde Vries (EKdV) equation. This equation displays undular bores upstream in a subcritical regime, but monotonic bores in a transcritical regime. The monotonic bores are solitary wave solutions of the corresponding homogeneous EKdV equation. Again, locally steady flow is attained for sufficiently large supercritical Froude numbers. The predictions of the numerical solutions are compared with laboratory experiments which show good agreement with the solutions of the forced EKdV equation for some range of parameters. It is shown that a recent result of Miles (1986), which predicts an unsteady transcritical regime for single-layer flows, may readily be extended to two-layer flows (described by the forced KdV equation) and is in agreement with the results presented here.Numerical experiments exploiting the symmetry of the homogeneous EKdV equation show that solitary waves of fixed amplitude but arbitrary length may be generated in systems described by the inhomogeneous EKdV equation.

Sign in / Sign up

Export Citation Format

Share Document