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

Abstract

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

Keywords:

• Generalized Korteweg-deVries equation
• existence
• nonconstant periode traveling wave solution
• 35B10
• 35Q20

AMS(MOS)::

• 35B10
• 35Q20