Conservation laws of the complex Ginzburg-Landau equation

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].…”

Global Weak Solution for Phase Transition Equations with Polarization

“…There has recently been a lot of progress in the study and development of the theory of the paramagnetic-ferromagnetic transition [3][4][5][6][7][8]. In [5,6], Berti proposes a model for the dynamics of a magnetization vector in a ferromagnetic body.…”