Abstract
Analysis of short-pulse propagation in positive dispersion media for example in optical fibers and in shallow water, requires assorted high-order derivative terms. The different dynamical features underlying soliton interactions in the generalized higher-order nonlinear Schrödinger equation, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, the new exact solitary solutions in generalized form of generalized higher-order nonlinear Schrödinger equation (NLSE) are constructed with the aid of symbolic computation by employing modified extended direct algebraic method. The complex physical phenomena of generalized higher-order NLSE can be understand from the obtained solutions. The computational work shows that the current method is simple, general, powerful, effective, and wider applicable. Moreover, several new complex higher-order NLSEs that arising in mathematical physics can also be solved by this efficient method.