Physics, mathematics, and technology

2017 Issue №1

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An impacton solution for the vortex filament



A new way of construction of exact solutions describing the shape and the dynamics of vortex filaments is described. The new method is based on application of a binary Darboux transformation to the solutions of the nonlinear Schrödinger equation. A new type of solutions is constructed: the impacton. The explicit form of the curvature and torsion of corresponding vortex filament are calculated.


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