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Full-Text Articles in Physical Sciences and Mathematics
Interactions And Focusing Of Nonlinear Water Waves, Harihar Khanal, S.C. Mancas, Shahrdad Sajjadi
Interactions And Focusing Of Nonlinear Water Waves, Harihar Khanal, S.C. Mancas, Shahrdad Sajjadi
Publications
A theoretical and computational study is undertaken for the modulational instabilities of a pair of nonlinearly interacting two-dimensional waves in deep water. It has been shown that the full dynamics of these interacting waves gives rise to localized large-amplitude wavepackets (wave focusing). The coupled cubic nonlinear Schrödinger (CNLS) equations are used to derive a nonlinear dispersion equation which give rise to new class of modulational instabilities and demonstrates the dependence of obliqueness of the interacting waves. The computations, due to nonlinear wave-wave interactions, waves that are separately modulationally stable can give rise to the formation of large-amplitude coherent wave packets …
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 …