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Full-Text Articles in Physical Sciences and Mathematics
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 …
Solitary Waves, Periodic And Elliptic Solutions To The Benjamin, Bona & Mahony (Bbm) Equation Modified By Viscosity, S.C. Mancas, Harihar Khanal, Shahrdad G. Sajjadi
Solitary Waves, Periodic And Elliptic Solutions To The Benjamin, Bona & Mahony (Bbm) Equation Modified By Viscosity, S.C. Mancas, Harihar Khanal, Shahrdad G. Sajjadi
Publications
We introduce spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in which asymmetry between space-time variables is included. The 2D CCQGLE is solved by a powerful Fourier spectral method, i.e., a Fourier spatial discretization and an explicit scheme for time differencing. Varying the system’s parameters, and using different initial conditions, numerical simulations reveal 2D solitons in the form of stationary, pulsating and exploding solitons which possess very distinctive properties. For certain region of parameters, we have also found stable coherent structures in the form of spinning (vortex) solitons which exist as a result …
Numerical Simulations Of Snake Dissipative Solitons In Complex Cubic-Quintic Ginzburg-Landau Equation, S.C. Mancas, Harihar Khanal
Numerical Simulations Of Snake Dissipative Solitons In Complex Cubic-Quintic Ginzburg-Landau Equation, S.C. Mancas, Harihar Khanal
Publications
Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal five entirely novel classes of pulse or solitary waves solutions, viz. pulsating, creeping, snaking, erupting, and chaotical solitons. Here, we develop a theoretical framework for analyzing the full spatio-temporal structure of one class of dissipative solution (snaking soliton) of the CCQGLE using the variational approximation technique and the dynamical systems theory. The qualitative behavior of the snaking soliton is investigated using the numerical simulations of (a) the full nonlinear complex partial differential equation …
Nonlinear Equations And Wavelets, Andrei Ludu