Classical Solutions for the Generalized Korteweg-de Vries Equation

The Korteweg-de Vries equation models the formation of solitary waves in context shallow water a channel. In Equation (1), f or p=2 and p=3 (Korteweg-de equations (KdV)) (modified (mKdV) respectively), these have many applications Physics. (gKdV) is Hamiltonian system. this article we investigate generalized (3). A new topological approach applied to prove existence at least one classical solution. arguments are based upon recent theoretical results.