Collisions of matter-wave solitons
  Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass through one another and emerge from the collision unaltered in shape, amplitude, or velocity. This remarkable property is mathematically a consequence of the underlying integrability of the one-dimensional (1D) equations, such as the nonlinear Schr\"odinger equation, that describe solitons in a variety of wave contexts, including matter-waves$^{1,2}$. Here we explore the nature of soliton collisions using Bose-Einstein condensates of atoms with attractive interactions confined to a quasi-one-dimensional waveguide. We show by real-time imaging that a collision between solitons is a complex event that differs markedly depending on the relative phase between the solitons. Yet, they emerge from the collision unaltered in shape or amplitude, but with a new trajectory reflecting a discontinuous jump. By controlling the strength of the nonlinearity we shed new light on these fundamental features of soliton collisional dynamics, and explore the implications of collisions that bring the wave packets out of the realm of integrability, where they may undergo catastrophic collapse.   1. Zabusky, N.J. & Kruskal, M.D. Interaction of "solitons" in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15, 240 (1965).   2. Zakharov, V.E. & Shabat, A.B. Exact theory of two-dimensional self-focusing and one-dimensional self-moduation of waves in nonlinear media. Sov. Phys. JEPT. 34, 62 (1972). 
Jason H.V. Nguyen, Paul Dyke, De Luo, Boris A. Malomed and Randall G.   Hulet
cond-mat.quant-gas nlin.PS