Time-independent harmonics dispersion relation for time-evolving nonlinear waves
Romik Khajehtourian, Mahmoud I. Hussein
Abstract
) solution. It is valid throughout the evolution of a distorting unbalanced wave or the steady-steady propagation of a balanced wave with waveform invariance. The new relation is shown to be a special case of the general nonlinear dispersion relation (NDR), which is also derived. The theory is examined on a diverse range of cases of one-dimensional elastic waves and shown to hold irrespective of the spatial form of the initial wave profile, type and strength of the nonlinearity, and the level of dispersion in the linear limit. Another direct outcome of the general NDR is an analytical condition for soliton synthesis.
Topics & Concepts
HarmonicsDispersion relationDispersion (optics)Nonlinear systemPhysicsWaveformWave propagationMathematical analysisRange (aeronautics)Limit (mathematics)Classical mechanicsMathematicsOpticsQuantum mechanicsMaterials scienceVoltageComposite materialNonlinear Photonic SystemsNonlinear Waves and SolitonsAdvanced Fiber Laser Technologies