11 research outputs found
From nonassociativity to solutions of the KP hierarchy
A recently observed relation between 'weakly nonassociative' algebras A (for
which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent
variable in the middle nucleus A' of A) is recalled. For any such algebra there
is a nonassociative hierarchy of ODEs, the solutions of which determine
solutions of the KP hierarchy. In a special case, and with A' a matrix algebra,
this becomes a matrix Riccati hierarchy which is easily solved. The matrix
solution then leads to solutions of the scalar KP hierarchy. We discuss some
classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and
Quantum Symmetries', Prague, 15-17 June 200
Dynamics of Dark-Bright Solitons in Cigar-Shaped Bose-Einstein Condensates
We explore the stability and dynamics of dark-bright solitons in
two-component elongated Bose-Einstein condensates by developing effective 1D
vector equations as well as solving the corresponding 3D Gross-Pitaevskii
equations. A strong dependence of the oscillation frequency and of the
stability of the dark-bright (DB) soliton on the atom number of its components
is found. Spontaneous symmetry breaking leads to oscillatory dynamics in the
transverse degrees of freedom for a large occupation of the component
supporting the dark soliton. Moreover, the interactions of two DB solitons are
investigated with special emphasis on the importance of their relative phases.
Experimental results showcasing dark-bright soliton dynamics and collisions in
a BEC consisting of two hyperfine states of Rb confined in an elongated
optical dipole trap are presented.Comment: 4 pages, 5 figure