Chaos of 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 the famous Lorenz system and its general form from the DS equation and the ANNV equation. Some types of chaotic soliton solutions can be obtained from analytic expression of higher dimensional soliton systems and the numeric results of lower dimensional chaos systems. 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 In the past three decades, both the solitons [1] and the chaos[2] have been widely studied and applied in many natural sciences 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 considers 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 especially in higher dimensions. When one says a model is integrable, one should emphasize two important facts. The first one is that we should point out the model is integrable under what special meaning(s). For instance, we say a model is Painlevé integrable if the model Email: [email protected] Mailing address