On existence theorems of periodic traveling wave solutions to the two-dimensional korteweg-devries equation

The two-dimensional generalized Korteweg-deVries equation is considered. We show the existence of nonconstant periodic traveling wave solutions. The equation is converted into a nonlinear integral equation using the Green's function method. We then employ the Schauder's fixed point theorem to establish the result. An example is given for the case of f(u) = 2u 3,i.e., the modified KdV equation