Abstract
In this paper we use bifurcation methods to construct a new family of solutions of the binormal flow, also known as the vortex filament equation, which do not change their form. Our examples are complementary to those obtain by S. Kida in 1981, and therefore they are also related, thanks to the so-called Hasimoto transformation, to traveling wave solutions of the 1d cubic non-linear Schrödinger equation.
Disclosure statement
The authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this manuscript. Moreover, data sharing not applicable to this article as no datasets were generated or analyzed during the current study.