Conservation laws and Hamiltonians of the mathematical model with unrestricted dispersion and polynomial nonlinearity

Bifurcations of Phase Portraits, Exact Solutions and Conservation Laws of the Generalized Gerdjikov–Ivanov Model

“…In this section, we find three conservation laws corresponding to Equation (1). In order to look for these laws, we write Equation (1) as the system of equations of the form (see, for example, [36])…”

Soliton solutions of the improved perturbed nonlinear Schrödinger equation having parabolic law with non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion terms

“…The use of the NLSE in many application areas, especially modeling ultrashort pulse propagation in optical fibers, modeling the behavior in quantum gases, explaining the behavior of wave guides and optical solitons, modeling waves in plasma physics, understanding and improving the performance of fiber optic sensors and laser systems, is considered a powerful tool for modeling and understanding complex physical processes [1][2][3][4]. Investigating analytical solutions of the NLSE provides a deeper understanding of the formation, evolution, and interactions of optical solitons, as well as enabling theoretical predictions about the behavior of specific physical systems [5][6][7][8][9][10][11][12][13]. Therefore, different methods have been improved to produce analytical solutions of the NLSE like the new Kudryashov scheme [14][15][16], the improved generalized Kudryashov method [17], enhanced modified extended tanh application [18][19][20], modified simple equation technique [21,22] and the F-expansion technique [23,24].…”