This paper carries out the integration of the resonant nonlinear Schrödinger’s equation in presence of perturbation terms that are considered with full nonlinearity. The three types of nonlinear media are studied. They are the cubic nonlinearity, power law and log law nonlinearity. The semi-inverse variational principle is applied to extract the analytical soliton solution.

We study the inverse scattering problem for the three dimensional nonlinear Schrödinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of the scattering states. Our result is applicable to reconstructing the nonlinearity of the semi-relativistic Hartree equation.

Functions with high nonlinearity have important applications in cryptography se quences and coding theory The purpose of this paper is to give a well rounded treatment of non Boolean functions with optimal nonlinearity We summarize and generalize known results and prove a number of new results We also present open problems about functions with high nonlinearity