Nonlinear evolution of modulational instability by using the nonlinear Schrödinger equation in one dimension reveals a periodic reoccurrence of initial conditions. The nonlinear Schrödinger equation is the adiabatic limit of Zakharov equations, which couples the electrostatic electron plasma wave and ion-acoustic wave propagation. In the present paper nonlinear evolution of modulational instability is investigated by using one-dimensional Zakharov equations numerically. A simplified model is predicted that establishes the fact that the effect of relaxing the condition of adiabaticity is drastic on the nonlinear evolution patterns of modulational instability. These evolutions are quite sensitive to initial conditions, Fermi–Pasta–Ulam recurrence is broken up and a chaotic state develops. Next, quantitative methods like calculation of Lyapunov exponents and their variation with wave number is used to study spatial and temporally chaotic behavior. It is shown that regular patterns with a periodic sequence in space and time and spatiotemporal chaos with irregular localized patterns are formed in different regions of unstable wave numbers
Published online by Cambridge University Press 08Mar2006International audienceIn the present paper the long-term behavior of the nonlinear dynamical evolution of modulational instability is investigated by using a simplified model for one-dimensional Zakharov equations, which couples the electrostatic electron plasma wave and ion-acoustic wave propagation. The manuscript details on the occurrence of fixed points and fixed-point attractors for a suitable value of the wavenumber of perturbation through associated bifurcations, both for the adiabatic (nonlinear Schrödinger equation) and non-adiabatic cases for Zakharov equations. It is shown that these evolutions are quite sensitive to initial conditions, Fermi–Pasta–Ulam recurrence is broken up and a chaotic state develops for the non-adiabatic case. Regular patterns with a periodic sequence in space and time and spatiotemporal chaos with irregular localized patterns are formed in different regions of unstable wavenumbers, hence producing a self-organizing dynamical system. The results are consistent with those obtained by numerically solving Zakharov equations as previously reported and summarized in the present manuscript
We present a theory of slow self-focusing that is paraxial in nature, gives the field including the phase and eikonal explicitly, while it also agrees with the results of variational and moments theories. After presenting the features of the theory, particularly its similarity to the central force problem, we go on to reformulate the theory for an absorbing medium. We find that the laser beam focuses to a constant beamwidth with a small phase-front curvature depending on the extent of absorption. The theory is applicable to a whole range of saturating nonlinearities although it specializes to two plasma cases, the ponderomotive force based and the relativistic electron quiver based nonlinearities, for definitive results.
[1] This work presents the numerical simulation of the nonlinear evolution of kinetic Alfvén wave (KAW), in a parametric regime consistent with the solar wind plasmas. The nonlinear dynamical equation of KAW satisfies the modified nonlinear Schrödinger equation when incident pump KAW has a small perturbation. Numerical simulation has been done to solve this model equation when the ponderomotive nonlinearity is incorporated in the KAW dynamics. The localization of pump KAW as a consequence of ponderomotive nonlinearity has been studied in the solar wind at 1 AU. A weak whistler signal propagating in these localized structures is amplified and leads to the development of its own localized structures. Magnetic power spectra and spectral indices for KAW at different times are calculated. The magnetic field power spectra and spectral indices of whistler wave at different times are also calculated. The relevance of steepened KAW and whistler spectra to recent solar wind observations is also pointed out. These localized structures and steeper spectra can be responsible for the plasma heating and particles acceleration in solar wind.Citation: Dwivedi, N. K., K. Batra, and R. P. Sharma (2012), Study of kinetic Alfvén wave and whistler wave spectra and their implication in solar wind plasma,
Theoretical analysis is presented of the nonlinear behavior of charge carriers in biological tissue under the influence of varying low-intensity electromagnetic (EM) field. The interaction occurs because of the nonlinear force arising due to the gradient of the EM field intensity acting on free electrons in the conduction band of proteins in metabolically active biological cell membrane receptors leading to a redistribution of charge carriers. Field dependence of the resulting dielectric constant is investigated by a suitable modification to include an additional electronic contribution term to the three-term Debye model. The exogenous EM field propagating in this nonlinear cellular medium satisfies the nonlinear Schrödinger equation and can be affected significantly. Resulting field effect can be substantially augmented and effective rectification/demodulation can occur. Possible implications of this modification on biological processes in white and grey matter are discussed.
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