A ug 2 00 6 A theory for one dimensional asynchronous chemical wave

We present a theory for experimentally observed phenomenon of one dimensional asynchronous waves. The general principle of coexistence of linear and nonlinear solutions of a dynamical system is underlying the present theoretical work. The result has been proposed analytically and numerical simulations are produced in support of the analytical results. One dimensional asynchronous chemical waves (or 1d spirals) were first reported by J.-J.Perraud et al [1] in 1993. An explanation of this phenomenon had been put forward on the basis of bi-stability of Turing and Hopf states and non-variational effects. Historically, in those days when the above mentioned experiment was done, studying droplet of other states inside a global one under uniform conditions was a topic of tremendous interest. Mainly being influenced by those new observations [2, 3, 4, 5] and some numerically simulated asynchronous wave like structures, the bi-stability of Turing and Hopf modes and their interaction was considered to be the basic underlying principle on which a possible explanation of experimentally observed 1d spirals was given. Such localized droplets of global states near a Hopf-Turing instability boundary have been analyzed in many subsequent papers [6-12]. As a result of considering bi-stability the dynamics was considered not to derive form variational principle [1]. Since any other alternative theory is not present, the above mentioned mechanism is till date considered as the basis for such a novel phenomenon of nonlinear waves. In the present letter we are going to demonstrate an alternative scenario for 1D spiral generation. In what follows we will show that sustenance of parity inverted global traveling wave states require the presence of a class of asymmetric localized structures. We show that the mechanism of generation of 1d asynchronous waves is intrinsic to the type of amplitude equation valid close to a *