1306.0300 (Andrew Koller et al.)

Intertwiners, SUSY Ladders, and the Transparency of Gross-Pitaevskii
Solitons to Bogoliubov Quasiparticles    [PDF]

Andrew Koller, Zaijong Hwang, Maxim Olshanii

In this Letter, we look at the phenomenon of the transparency of one-dimensional bright bosonic solitons to Bogoliubov excitations---at {\it all} energies. Physically, this phenomenom underlies the ability of the Bogoliubov-de Gennes equation to describe collisions of small solitons of the nonlinear Schr\"odinger equation on large ones. Mathematically, the transparency at all energies suggests some non-trivial property of the equations involved. Indeed, we uncover an interwining structure that constitutes a powerful generalization of quantum-mechanical supersymmetry. We extend our findings to the sine-Gordon and Korteweg-de Vries equations, and discover a new instance of scattering without reflection in the latter case.

View original: http://arxiv.org/abs/1306.0300