SOLITONS IN THE COUPLED GENERALIZED NONLINEAR SСHRODINGER EQUATIONS - Serikbayev, N.S.; Shaikhova, G.N.; Belisarova, F.B. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2025)
Nonlinear equations essentially describe physical problems. Solitons, which are localized in space and time and propagate in a nonlinear medium, are the special specific solutions to some of these equations. The soliton remerges after a fully nonlinear interaction, retaining their identities with the same speed and shape. It has remarkable stability properties. Stability plays an important role in soliton physics. The nonlinear Schrodinger equation, one of the soliton-type nonlinear equations, is notable for its significance in the theory of nonlinear waves, specifically in nonlinear optics and plasma physics. The investigation of nonlinear Schrodinger equation generalizations is currently a pressing area of research. This work examines the coupled generalized nonlinear Schrodinger equations. These equations yield classical nonlinear Schrodinger equation in some reductions. As a research method, we use the bilinear Hirota method, which is one of the effective methods for solving nonlinear equations. Dispersion relations are derived and one-soliton and two-soliton solutions are obtained. The figures depict the dynamics of soliton solutions. From this research, the results obtained may be useful for a better understanding of the nonlinear wave phenomena in any varied instance where the coupled model considered is applicable.