scholarly journals Controllability result for nonlinear evolution integrodifferential systems

2004 ◽  
Vol 17 (9) ◽  
pp. 1015-1023 ◽  
Author(s):  
R. Sakthivel ◽  
Q.H. Choi ◽  
S.M. Anthony
Keyword(s):  
Nonlinear Evolution ◽  
Controllability Result

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

Instabilities of Jets and Fronts and their Nonlinear Evolution

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Trapped Modes ◽  
Nonlinear Saturation ◽  
Parallel Flows ◽  
Inertial Instability ◽  
Shear Instabilities ◽  
Linear And Nonlinear ◽  
Flow Configurations ◽  
Characteristic Features

Notions of linear and nonlinear hydrodynamic (in)stability are explained and criteria of instability of plane-parallel flows are presented. Instabilities of jets are investigated by direct pseudospectral collocation method in various flow configurations, starting from the classical barotropic and baroclinic instabilities. Characteristic features of instabilities are displayed, as well as typical patterns of their nonlinear saturation. It is shown that in the Phillips model of Chapter 5, new ageostrophic Rossby–Kelvin and shear instabilities appear at finite Rossby numbers. These instabilities are interpreted in terms of resonances among waves counter-propagating in the flow. It is demonstrated that the classical inertial instability is a specific case of ageostrophic baroclinic instability. At the equator it appears also in the barotropic configuration, and is related to resonances of Yanai waves. The nature of the inertial instability in terms of trapped modes is established. A variety of instabilities of density fronts is displayed.

The Stability of Radiatively Cooling Jets. II. Nonlinear Evolution

1997 ◽  
Vol 483 (1) ◽  
pp. 136-147 ◽  
Author(s):  
James M. Stone ◽  
Jianjun Xu ◽  
Philip E. Hardee
Keyword(s):  
Nonlinear Evolution ◽  
The Stability

scholarly journals Effects of plasma turbulence on the nonlinear evolution of magnetic island in tokamak

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Minjun J. Choi ◽  
Lāszlo Bardōczi ◽  
Jae-Min Kwon ◽  
T. S. Hahm ◽  
Hyeon K. Park ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Nonlinear Evolution ◽  
Plasma Turbulence ◽  
Magnetized Plasmas ◽  
Tokamak Plasmas ◽  
Magnetic Islands ◽  
Magnetic Island ◽  
Reconnection Site ◽  
Ambient Turbulence

AbstractMagnetic islands (MIs), resulting from a magnetic field reconnection, are ubiquitous structures in magnetized plasmas. In tokamak plasmas, recent researches suggested that the interaction between an MI and ambient turbulence can be important for the nonlinear MI evolution, but a lack of detailed experimental observations and analyses has prevented further understanding. Here, we provide comprehensive observations such as turbulence spreading into an MI and turbulence enhancement at the reconnection site, elucidating intricate effects of plasma turbulence on the nonlinear MI evolution.

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