New geometries associated with the nonlinear Schrödinger equation
The Institute of Mathematical Sciences, Chennai 600 113, India
Corresponding author: a email@example.com
Published online: 2 October 2002
We apply our recent formalism establishing new connections between the geometry of moving space curves and soliton equations, to the nonlinear Schrödinger equation (NLS). We show that any given solution of the NLS gets associated with three distinct space curve evolutions. The tangent vector of the first of these curves, the binormal vector of the second and the normal vector of the third, are shown to satisfy the integrable Landau-Lifshitz (LL) equation , (). These connections enable us to find the three surfaces swept out by the moving curves associated with the NLS. As an example, surfaces corresponding to a stationary envelope soliton solution of the NLS are obtained.
PACS: 02.40.Hw – Classical differential geometry / 05.45.Yv – Solitons / 75.10.Hk – Classical spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002