Envelope compacton and solitary pattern solutions of a generalized nonlinear Schrödinger equation Original Research Article

In this paper, the generalized nonlinear Schrödinger equation with nonlinear dispersion View the MathML sourceiut+a(u|u|n−1)xx+bu|u|m−1=0 (called the View the MathML sourceGNLS(m,n) equation) is investigated by using the theory of a dynamical system. As a result, we obtain some envelope compacton and solitary pattern solutions of the View the MathML sourceGNLS(m,n) equation. In addition, we point out the reason for the appearance of the unsmooth solutions.