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Adiabatic Invariance III: The Equation x=−Vx(x, ω)

✍ Scribed by JE Littlewood

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
150 KB
Volume
281
Category
Article
ISSN
0003-4916

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✦ Synopsis

In the equation of the title |=|(t) is a slowly varying function of t for & 0, there is a ``momentary'' periodic motion between x=X$ and X, of period

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Differential invariants of nonlinear equ
Differential invariants of nonlinear equations vtt=f(x,vx)vxx+g(x,vx)
✍ N.H Ibragimov; M Torrisi; A Valenti 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 213 KB

We assumed in Theorem 2 that l 1 6 ¼ 0, where l 1 is the expression defined by Eq. ( 77). If l 1 ¼ 0, the corresponding Eq. ( 8) should be considered separately. Furthermore, the cases l 2 ¼ 0 and l 3 ¼ 0 (see Eqs. ( 78) and ( 79)) are also exceptional because of the following lemma: q