Nonlinear Waves and Solitons on Contours and Closed Surfaces by Andrei Ludu

Author:Andrei Ludu
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

2. If is the unit tangent for each Γ s curve, then ∀σ ∈ [0,σ max ]

is a regular parameterized surface for σ ∈ [0,σ max ],s ∈ [0,L Γ ].

Proof.

See Fig. 10.1. Since the field is differentiable, the curves Γs are its integral curves and depend smoothly on their natural arc-length parameter σ. Also, from the Frobenius existence and uniqueness theorem (Theorem 5), all these curves depend smoothly on their initial data, i.e., the s parameter (see also [46, Theorem 1, p. 176]). Consequently is a differentiable function. From the hypotheses each integral curve intersects the contour only one time. The Jacobian matrix

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.