Techniques for searching first integrals by Lie group and application to gyroscope system

Hu, Yanxia; Ke-ying, Guan

doi:10.1360/04ys0141

Cited by 16 publications

(6 citation statements)

References 4 publications

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“…We can let b1 = 1, b0 = 0, and get the solution f1, f2, f3 from the corresponding algebraic system [20], …”

Section: The First Integral Under Thementioning

confidence: 99%

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The First Integrals of a Second Order Ordinary Differential Equation and Application

2019

AJRCoS

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The first integrals of second order ordinary differential equations are considered. The necessary conditions of the existence of analytical first integrals for the equation are presented. Then, the first integrals of the equation are obtained using Lie symmetry method. The results of the first integrals are applied to certain classes of partial differential equations, the conditions of nonexistence of the traveling wave solutions of the partial differential equations are obtained, and traveling wave solutions of the equations under the certain parametric conditions are also obtained.

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“…We can let b1 = 1, b0 = 0, and get the solution f1, f2, f3 from the corresponding algebraic system [20], …”

Section: The First Integral Under Thementioning

confidence: 99%

“…We can let b1 = 1, b0 = 0, and get the solution f1, f2, f3 from the corresponding algebraic system [20],    and a first integral Ω(x) of (3.9) is given by the following line integral…”

Section: The First Integral Under the Condition 6a 2 = −25cmentioning

confidence: 99%

The First Integrals of a Second Order Ordinary Differential Equation and Application

2019

AJRCoS

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Section: Introductionmentioning

confidence: 99%

“…Recently, several works have studied the integrability of autonomous systems and quasihomogeneous polynomial systems; for more details see [1][2][3][4][5][6]. In [5], several techniques for searching first integrals of nth autonomous systems by using Lie groups admitted by the systems are proposed. The integrability of quasihomogeneous planar systems is studied in [1,3], and the existence of a link between the Kowalevskaya exponents of quasihomogeneous systems and the degree of their quasihomogeneous polynomial first integrals is studied in [2,4].…”

Section: Introductionmentioning

confidence: 99%

“…The integrability of quasihomogeneous planar systems is studied in [1,3], and the existence of a link between the Kowalevskaya exponents of quasihomogeneous systems and the degree of their quasihomogeneous polynomial first integrals is studied in [2,4]. There exist some methods for studying the integrability of autonomous systems by using Lie group admitted by the systems [5,7,8] and using by the invariant manifolds of the systems [6]. As we know, the existence of inverse integrating factors gives a lot of information on dynamics, integrability of the systems and so on.…”

Section: Introductionmentioning

confidence: 99%

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On the Integrability of Quasihomogeneous Systems and Quasidegenerate Infinity Systems

2007

Adv. Differ Equ.

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The integrability of quasihomogeneous systems is considered, and the properties of the first integrals and the inverse integrating factors of such systems are shown. By solving the systems of ordinary differential equations which are established by using the vector fields of the quasihomogeneous systems, one can obtain an inverse integrating factor of the systems. Moreover, the integrability of a class of systems (quasidegenerate infinity systems) which generalize the so-called degenerate infinity vector fields is considered, and a method how to obtain an inverse integrating factor of the systems from the first integrals of the corresponding quasihomogeneous systems is shown.

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One-parameter Lie groups and inverse integrating factors of n-th order autonomous systems

Xue

2012

Journal of Mathematical Analysis and Applications

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Techniques for searching first integrals by Lie group and application to gyroscope system

Cited by 16 publications

References 4 publications

The First Integrals of a Second Order Ordinary Differential Equation and Application

The First Integrals of a Second Order Ordinary Differential Equation and Application

On the Integrability of Quasihomogeneous Systems and Quasidegenerate Infinity Systems

One-parameter Lie groups and inverse integrating factors of n-th order autonomous systems

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