It is known that classical string dynamics in pure AdS_5\times S^5 is
integrable and plays an important role in solvability. This is a deep and
central issue in holography. Here we investigate similar classical
integrability for a more realistic confining background and provide a negative
answer. The dynamics of a class of simple string configurations in AdS soliton
background can be mapped to the dynamics of a set of non-linearly coupled
oscillators. In a suitable limit of small fluctuations we discuss a
quasi-periodic analytic solution of the system. However numerics indicates
chaotic behavior as the fluctuations are not small. Integrability implies the
existence of a regular foliation of the phase space by invariant manifolds. Our
numerics shows how this nice foliation structure is eventually lost due to
chaotic motion. We also verify a positive Lyapunov index for chaotic orbits.
Our dynamics is roughly similar to other known non-integrable coupled
oscillators systems like Henon-Heiles equations.Comment: Acknowledged grant