Two-Component Generalization of a Generalized the Short Pulse Equation

2019 ◽  
pp. 1760-1765
Author(s):  
Mohammed Allami
Keyword(s):  
Nonlinear Equations ◽  
Short Pulse ◽  
Three Dimensional ◽  
Continuous Group ◽  
System Of Nonlinear Equations ◽  
Similarity Reduction ◽  
Short Pulse Equation ◽  
Point Transformations ◽  
Two Component ◽  
Lie Brackets

     In this article, we introduce a two-component generalization for a new generalization type of the short pulse equation was recently found by Hone and his collaborators. The coupled of nonlinear equations is analyzed from the viewpoint of Lie’s method of a continuous group of point transformations. Our results show the symmetries that the system of nonlinear equations can admit, as well as the admitting of the three-dimensional Lie algebra. Moreover, the Lie brackets for the independent vectors field are presented. Similarity reduction for the system is also discussed.

scholarly journals On integrability of the Yao–Zeng two-component short-pulse equation

2012 ◽  
Vol 377 (1-2) ◽  
pp. 80-82 ◽  
Author(s):  
J.C. Brunelli ◽  
S. Sakovich
Keyword(s):  
Short Pulse ◽  
Short Pulse Equation ◽  
Two Component

A Precise and Efficient Method to Manipulate the Amplitude of Parabolic Function of Transmission Errors

2014 ◽  
Vol 1064 ◽  
pp. 183-190
Author(s):  
Cheng Kang Lee
Keyword(s):  
Nonlinear Equations ◽  
Design Variable ◽  
Three Dimensional ◽  
Spur Gear ◽  
System Of Nonlinear Equations ◽  
Unknown Parameters ◽  
Transmission Errors ◽  
Root Finding ◽  
Parabolic Function ◽  
Root Finding Method

This paper proposes a system of nonlinear equations to manipulate the amplitude of parabolic function of transmission errors. Firstly, the characteristics of parabolic function of transmission errors are defined. Then, a system of nonlinear equations for manipulating the amplitude of parabolic function of transmission errors is created based on both the conditions of contact and the constraint on the amplitude of function of transmission errors. As the number of independent scalar equations in the system minus the number of unknown parameters is one, one extra design parameter can be applied to manipulate the amplitude of parabolic function of transmission errors. The solution to the extra design variable is automatically, precisely, and efficiently determined by the computer program which is created based on the Newton’s root finding method. The time-consuming manual iterations for trying the value of design variable are eliminated. The proposed method can be applied to both two-and three-dimensional gearing problems. At last, a pair of meshing gears composed of a circular-arc spur gear and an involute spur gear is presented to verify the methodology proposed in this paper.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations

Soliton resolution for the short-pulse equation

2021 ◽  
Vol 280 ◽  
pp. 644-689
Author(s):  
Yiling Yang ◽  
Engui Fan
Keyword(s):  
Short Pulse ◽  
Short Pulse Equation

scholarly journals Target alignment in the Shen-Guang II Upgrade laser facility

2018 ◽  
Vol 6 ◽  
Author(s):  
Lei Ren ◽  
Ping Shao ◽  
Dongfeng Zhao ◽  
Yang Zhou ◽  
Zhijian Cai ◽  
...  
Keyword(s):  
Inertial Confinement Fusion ◽  
Short Pulse ◽  
Three Dimensional ◽  
Nanosecond Laser ◽  
Alignment Error ◽  
Inertial Confinement ◽  
Pulse Beam ◽  
Rotation Sensor ◽  
Confinement Fusion ◽  
Laser Facility

The Shen-Guang II Upgrade (SG-II-U) laser facility consists of eight high-power nanosecond laser beams and one short-pulse picosecond petawatt laser. It is designed for the study of inertial confinement fusion (ICF), especially for conducting fast ignition (FI) research in China and other basic science experiments. To perform FI successfully with hohlraum targets containing a golden cone, the long-pulse beam and cylindrical hohlraum as well as the short-pulse beam and cone target alignment must satisfy tight specifications (30 and $20~\unicode[STIX]{x03BC}\text{m}$ rms for each case). To explore new ICF ignition targets with six laser entrance holes (LEHs), a rotation sensor was adapted to meet the requirements of a three-dimensional target and correct beam alignment. In this paper, the strategy for aligning the nanosecond beam based on target alignment sensor (TAS) is introduced and improved to meet requirements of the picosecond lasers and the new six LEHs hohlraum targets in the SG-II-U facility. The expected performance of the alignment system is presented, and the alignment error is also discussed.

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