Perturbation methods in group analysis

Байков, В. А.; Газизов, Р. К.; Ibragimov, N. Kh.

doi:10.1007/bf01097534

Cited by 88 publications

(68 citation statements)

References 6 publications

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“…The next step in our algorithm is to find X 1 (which we will call Y to avoid confusion with subscripts), such that which is exactly the same set of determining equations that the method of Baikov et al [6,7] gives, so from here on, the calculations are identical. For further discussions on potential symmetries, the reader may refer to [8,9].…”

Section: Letmentioning

confidence: 99%

Symmetries and Differential Forms

Davison¹,

Kara²

2008

JNMP

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Section: Letmentioning

confidence: 99%

Symmetries and Differential Forms

Davison¹,

Kara²

2008

JNMP

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“…al. [1,2]. Another approach is that of finding approximate conditional symmetries admitted by the model equation as presented by Mahomed and Qu [13].…”

Section: Copyright C 2002 By E Momoniatmentioning

confidence: 99%

Approximate Waiting-Time for a Thin Liquid Drop Spreading under Gravity

Momoniat

2002

JNMP

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The method of multiple scales is used to introduce a small-time scale into the nonlinear diffusion equation modelling the spreading of a thin liquid drop under gravity. The Lie group method is used to analyse the resulting system. An approximate group invariant solution and an approximation to the waiting-time is obtained. A mathematical description of a spreading drop with non-infinite contact angle is obtained. This application to determining an approximation to the waiting-time is novel as it combines the method of multiple scales and Lie groups.

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“…Therefore, perturbation to symmetry and adiabatic invariants became a popular subject recently. The notion of approximate conservation laws was introduced with regards to approximate Noether symmetry by Baikov et al [28]; Kara et al [29,30] extended Baikov's ideas. Fu and Chen et al [31,32] studied the perturbation to the Lie symmetry and adiabatic invariants.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the definition of adiabatic invariants, the relationship of perturbation to symmetry with adiabatic invariants are constructed. It offers an opportunity for the quasi-integrability in dynamical systems [26,27]. Therefore, perturbation to symmetry and adiabatic invariants became a popular subject recently.…”

Section: Introductionmentioning

confidence: 99%