Solitary Waves, Periodic and Elliptic Solutions to the Benjamin, Bona & Mahony (BBM) Equation Modified by Viscosity
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 of a competition between focusing nonlinearities and spreading while propagating through medium.
Advances and Applications in Fluid Dynamics
Pushpa Publishing House
Scholarly Commons Citation
Mancas, S., Khanal, H., & Sajjadi, S. G. (2011). Solitary Waves, Periodic and Elliptic Solutions to the Benjamin, Bona & Mahony (BBM) Equation Modified by Viscosity. Advances and Applications in Fluid Dynamics, 9(1). Retrieved from https://commons.erau.edu/publication/776