Daniil R. Nifontov1, Olga A. Fuga, Nikolay A. Kudryashov
Department of Applied Mathematics National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 31 Kashirskoe Shosse, 115409 Moscow, Russian Federation
Received 8 August, 2025; accepted in revised form 14 August 2026
Abstract: The generalized Hasegawa-Kodama equation is considered. This equation is used to describe the propagation of pulses in nonlinear optical media. The studied equation generalizes the classical nonlinear Schrödinger equation. The generalized Hasegawa-Kodama equation accounts for complex nonlinear effects in the description of pulse propagation in nonlinear optical media. Conservation laws and corresponding first integrals for the equation under study have been constructed. Some exact solutions of the generalized Hasegawa-Kodama equation have been obtained. The derived solutions exhibit periodic behavior or take the form of optical solitons. Conserved quantities for solitary waves have been computed. The computed conserved quantities are used to verify the results of numerical
simulations of optical pulses. The results of this work have practical significance for evaluating pulse parameters in nonlinear media.
© 2006 European Society of Computational Methods in Sciences and Engineering
Keywords: Hasegawa-Kodama equation; Optical solitons; Conservation laws; Nonlinear optics; Conserved quantities Mathematics Subject Classification: 35Q55