Local well-posedness of a generalized nonlinear Schrödinger equation with cubic–quintic nonlinearity

Abstract

In this article, we study the Cauchy Problem associated to the generalized cubic–quintic Schrödinger equation which has been used for the description of propagation pulses in optical fibers. Using gauge transforms and a derivation process, we prove under some regularity assumptions, the local well-posedness. Additionally, a global H1 bound is established for the solution.