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- W2188545105 abstract "The single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant is fundamentally a result of the corresponding symmetry admitted by the oscillator equation with timedependent frequency. A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method." @default.
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- W2188545105 date "2005-01-01" @default.
- W2188545105 modified "2023-09-27" @default.
- W2188545105 title "elope Equation SYMMETRIES AND INVARIANTS OF THE TIME-DEPENDENT OSCILLATOR EQUATION AND THE ENVELOPE EQUATION*" @default.
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