title: Solitons riding on solitons and the quantum Newton's cradle.
abstract: The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate an robust evolution of traveling hypersolitons. As an application to Bose-Einstein condensates trapped in a standard harmonic potential, we study the case of a finite dark soliton chain confined at the center of the trap. When the central chain is hit by a dark soliton, the energy is transferred through the chain as a hypersoliton that, in turn, ejects a dark soliton on the other end of the chain that, as it returns from its excursion up the trap, hits the central chain repeating the process. This periodic evolution is an analog of the classical Newton's cradle.
authors.affiliation: Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China.
authors.forename: Manjun
authors.initials: M
authors.lastname: Ma
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, MC 0411, La Jolla, California 92093-0411, USA.
authors.forename: R
authors.initials: R
authors.lastname: Navarro
authors.affiliation: Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720, USA.
authors.forename: R
authors.initials: R
authors.lastname: Carretero-González