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 solut...

In this article we consider nonlinear Schrödinger (NLS) equations in R for d = 1, 2, and 3. We consider nonlinearities satisfying a flatness condition at zero and such that solitary waves are stable. Let Rk(t, x) be K solitary wave solutions of the equation with different speeds v1, v2, . . . , vK . Provided that the relative speeds of the solitary waves vk − vk−1 are large enough and that no i...