REFERENCES
[1] S. V. Alekseenko, P. A. Kuibin, V. L. Okulov, Theory of concentrated vortices. An introduction,
Springer, Berlin, 2007.
[2] R. J. Arms and F. R. Hama, Localized-induction concept on a curved vortex and motion of
an elliptic vortex ring, Phys. Fluids 8 (1965), 553–559.
[3] R. Betchov, On the curvature and torsion of an isolated vortex filament, J. Fluid Mech. 22
(1965), 471–479.
[4] V. Banica and L. Vega, On the Dirac delta as initial condition for nonlinear Schr¨odinger
equations, Ann. Inst. H. Poincar´e Anal. Non Lin´eaire 25 (2008), no. 4, 697-711.
[5] V. Banica and L. Vega, On the stability of a singular vortex dynamics, Comm. Math. Phys
286 (2009), 593–627.
[6] V. Banica and L. Vega, Scattering for 1d Cubic NLS and Singular Vortex Dynamics, preprint
(2009).
[7] G. K. Batchelor, An Introduction to the Fluid Dynamics, Cambridge U. Press, Cambridge,
1967.
[8] T. F. Buttke, A numerical study of superfluid turbulence in the Self-Induction Approximation,
J. of Com. Phys. 76 (1988), 301–326.
[9] L. S. Da Rios, On the motion of an unbounded fluid with a vortex filament of any shape,
Rend. Circ. Mat. Palermo, 22 (1906), 117–135.
[10] S. Guti´errez and L. Vega, Self-similar solutions of the localized induction approximation: singularity
formation, Nonlinearity 17 (2004), 2091–2136.
[11] S. Guti´errez and L. Vega, On the stability of self-similar solutions of 1d cubic Schr¨odinger
equations, Preprint.
[12] S. Guti´errez, J. Rivas and L. Vega, Formation of singularities and self-similar vortex motion
under the localized induction approximation, Commun. Part. Diff. 28 (2003), 927–968.
[13] H. Hasimoto, A soliton on a vortex filament, J. Fluid Mech. 51 (1972), 477–485.
[14] A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow, Cambridge Texts in Applied
Mathematics, Cambridge U. Press, 2002.
[15] T. Lipniacki, Quasi-static solutions for quantum vortex motion under the localized induction
approximation, J. Fluid Mech. 477 (2003), 321–337.
[16] T. Lipniacki, Shape-preserving solutions for quantum vortex motion under localized induction
approximation, Physics of Fluids 15 (2003), 1381–1395.
[17] R. L. Ricca, The contributions of Da Rios and Levi-Civita to asymptotic potential theory and
vortex filament dynamics, Fluid Dynam. Res. 18 (1996), 245–268.
[18] R. L. Ricca, Physical interpretation of certain invariants for vortex filament motion under LIA,
Phys. Fluids A 4 (1992), 938–944.
[19] P. G. Saffman, Vortex Dynamics, Cambridge Monoghaps on Mechanics and Applied Mathematics,
Cambridge U. Press, New York 1992.
[20] K. W. Schwarz, Three-dimensional vortex dynamics in superfluid 4He: line-line and lineboundary
interactions, Phy. Rev B 31 (1985), 5782–5804.