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Full-Text Articles in Physical Sciences and Mathematics
Two-Dimensional Structures In The Quintic Ginzburg-Landau Equation, Florent Bérard, Charles-Julien Vandamme, S.C. Mancas
Two-Dimensional Structures In The Quintic Ginzburg-Landau Equation, Florent Bérard, Charles-Julien Vandamme, S.C. Mancas
Publications
By using ZEUS cluster at Embry-Riddle Aeronautical University we perform extensive numerical simulations based on a two-dimensional Fourier spectral method Fourier spatial discretization and an explicit scheme for time differencing) to find the range of existence of the spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation with cubic and quintic nonlinearities. We start from the parameters used by Akhmediev et. al. and slowly vary them one by one to determine the regimes where solitons exist as stable/unstable structures. We present eight classes of dissipative solitons from which six are known (stationary, pulsating, vortex spinning, filament, exploding, creeping) and two are …
Pulses And Snakes In Ginzburg-Landau Equation, S.C. Mancas, Roy S. Choudhury
Pulses And Snakes In Ginzburg-Landau Equation, S.C. Mancas, Roy S. Choudhury
Publications
Using a variational formulation for partial differential equations combined with numerical simulations on ordinary differential equations (ODEs), we find two categories (pulses and snakes) of dissipative solitons, and analyze the dependence of both their shape and stability on the physical parameters of the cubic-quintic Ginzburg–Landau equation (CGLE). In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. Numerical simulations reveal very interesting bifurcations sequences as the parameters of the CGLE …