N-soliton interactions in an extended Schrödinger equation with higher order of nonlinearities

We investigate the existence of N-solitons in an extended general nonlinear Schrödinger equation with third and fourth order dispersive terms that is most important for applications, such as the dynamics of a general class of anisotropic Heisenberg ferromagnetic spin chain with different magnetic interactions, the alpha helical proteins, and in media that offer interactions in biophysics. We have transformed the model to a homogeneous model that is utilized to show the existence of interactions of N-soliton solutions. We analyzed, and gave specific forms of these new class of N-solitons in a new simple form and discussed the interactions of these N-solitons. We have shown the existence of three types of head-on collisions, head-on collisions with or without over-taking or splitting into two solitons.