Displaced phase-amplitude variables for waves on finite background

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Groesen, E. van and Andonowati and Karjanto, N. (2006) Displaced phase-amplitude variables for waves on finite background. Physics Letters A, 354 (4). pp. 312-319. ISSN 0375-9601

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Abstract:Wave amplification in nonlinear dispersive wave equations may be caused by nonlinear focussing of waves from a certain background. In the model of nonlinear Schrödinger equation we will introduce a transformation to displaced phase-amplitude variables with respect to a background of monochromatic waves. The potential energy in the Hamiltonian then depends essentially on the phase. Looking as a special case to phases that are time independent, the oscillator equation for the signal at each position becomes autonomous, with the change of phase with position as only driving force for a spatial evolution towards extreme waves. This is observed to be the governing process of wave amplification in classes of already known solutions of NLS, namely the Akhmediev-, Ma- and Peregrine-solitons. We investigate the case of the soliton on finite background in detail in this Letter as the solution that descibes the complete spatial evolution of modulational instability from background to extreme waves.
Item Type:Article
Copyright:© 2006 Elsevier
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/57748
Official URL:http://dx.doi.org/10.1016/j.physleta.2006.02.037
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