### Abstract

A Lie group formalism for global parameter space mapping of ordinary differential equations, described in the preceding paper, is developed further here. The need for such mapping arises in a variety of physical contexts. The procedure is demonstrated on, but not restricted to, the system of coupled equations Ẋ = cX. The Lie group generators are obtained exactly from both the time-independent and time-dependent generating equations. The transformations obtained from these generators leave the system of differential equations invariant. The time-independent transformations map any solution of the linear system Ẋ = cX into any other solution with the same frequency or time constant. The time-dependent transformations interconvert solutions with different frequencies and/or time constants. Any solution of Ẋ = cX can be mapped into any solution of Ẋ = c′X. Thus the behavior of X (t) can be examined as a function of changes in any of the system parameters, or in the initial conditions, X(0). As an example, one of the time-dependent mappings demonstrates the continuous transformation of oscillator solutions into nonoscillatory ones, and vice versa.

Original language | English (US) |
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Pages (from-to) | 2273-2280 |

Number of pages | 8 |

Journal | The Journal of Physical Chemistry |

Volume | 90 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 1986 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)
- Physical and Theoretical Chemistry

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## Cite this

*The Journal of Physical Chemistry*,

*90*(10), 2273-2280. https://doi.org/10.1021/j100401a054