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Part I InternalWaves in Stratified Fluid
Part II Introduction to Lie Group Analysis
Part III Group Analysis of InternalWaves
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- 5.1 Preliminaries
- 5.1.1 Examples from elementary mathematics
- 5.1.2 Examples from physics
- 5.1.3 Examples from fluid mechanics
- 5.2 One-parameter groups
- 5.2.1 Introduction of transformation groups
- 5.2.2 Local one-parameter groups
- 5.2.3 Local groups in canonical parameter
- 5.3 Infinitesimal description of one-parameter groups
- 5.3.1 Infinitesimal transformation
- 5.3.2 Lie equations
- 5.3.3 Exponential map
- 5.4 Invariants and invariant equations
- 5.4.1 Invariants
- 5.4.2 Invariant equations
- 5.4.3 Canonical variables
- 5.4.4 Construction of groups using canonical variables
- 5.4.5 Frequently used groups in the plane
