Abstract
Using the simplest equation method, exact solutions of the model described by the fourth order generalized nonlinear Schrödinger equation with cubic-quintic-septic-nonic form of nonlinearity are obtained. Some of the main properties of the analytical model are established, such as dispersion relation, conservation of energy and linear instability. The split-step Fourier method is used to derive a numerical scheme for solving the model. The reflection of the properties of the analytical model in the numerical scheme is confirmed. Numerical simulations of the exact solutions of the model are performed, and approximation errors are measured. A numerical experiment is carried out on the interaction of two bright solitary waves.
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