Chaos in soliton systems and special Lax pairs for chaos systems

In this letter, taking the well known (2+1)-dimensional soliton systems, Davey-Stewartson (DS) model and the asymmetric Nizhnik-Novikov-Veselov (ANNV) model, as two special examples, we show that some types of lower dimensional chaotic behaviors may be found in higher dimensional soliton systems. Especially, we derive two famous chaotic system described by ordinary differential equation (ODE) systems, the Lorenz system and the “Brusselator” system, from the DS equation and write down a (1+1)-dimensional chaotic reduction, the generalized Lorenz system, from the ANNV equation. On the other hand, by means of the Lax pairs of some soliton systems, a lower dimensional chaos system may have some types of higher dimensional Lax pairs. An explicit (2+1)-dimensional Lax pair for a (1+1)dimensional chaotic equation is given. PACS numbers: 02.30.Ik, 05.45.-a, 05.45.Ac, 05.45.Jn, 42.65.Sf, 42.65.Tg, 52.35.Sb, 52.25Gj, 82.40.Bj In the past three decades, both the solitons[1] and the chaos[2] have been widely studied and applied in many natural sciences like the biology, chemistry, mathematics, communication and especially in almost all the physics branches such as the condense matter physics, field theory, fluid dynamics, plasma physics and optics etc. Usually, one considered that the solitons are the basic excitations of the integrable models and the chaos is the basic behavior of the nonintegrable models. Actually, the above consideration may not be complete. When one say a model is integrable, we should emphasize two important things. The first thing is we should Email: [email protected] Mailing address