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Full-Text Articles in Physical Sciences and Mathematics
Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, S.C. Mancas
Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, S.C. Mancas
Publications
From the works of authors of this article, it is known that the solution of the Ermakov equation is an important ingredient in the spectral problem of the Camassa-Holm equation. Here, we review this interesting issue and consider in addition more features of the Ermakov equation which have an impact on the behavior of the shallow water waves as described by the Camassa-Holm equation.
Spatiotemporal Two-Dimensional Solitons In The Complex Ginzburg-Landau Equation, Florent Berard, S.C. Mancas
Spatiotemporal Two-Dimensional Solitons In The Complex Ginzburg-Landau Equation, Florent Berard, S.C. Mancas
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 regions of parameters, we have also found stable coherent structures in the form of spinning (vortex) solitons which exist as a result …