Periodic traveling wave solutions for a coupled map lattice

A type of coupled map lattice (CML) is considered in this paper. What we want to do is to define the form of a traveling wave solution and to reveal its existence. Due to the infinite property of the problem, we have tried the periodic case, which can be dealt with on a finite set. The main approach for our study is the implicit existence theorem. The results indicate that if the parameters of the system satisfy some exact conditions, then there exists a periodic traveling wave solution in an exact neighborhood of a given one. However, these conditions are sufficient, but not necessary. In particular, the exact 2-periodic traveling wave solutions are also obtained. It gives some examples for the conditions of parameters, 2-periodic traveling wave solutions exist when these conditions are satisfied. Key–Words: Coupled map lattice, Periodic traveling wave solution, Implicit existence theorem, Nagumo equation, Nontrivial solution