Coefficients Of Nonlinear Schrodinger Equation Research Articles

Dust Charge Polarity Effect on Dust-Ion Acoustic Modulational Instability in a Nonthermal Dusty Plasma With Adiabatic Ions

The effects of dust charge polarity, ion temperature, and nonthermal electrons on dust-ion acoustic modulational instability and on the region (i.e., modulated wave number) for the formation of bright and dark envelope soliton structures are investigated. The dust particles are considered to be stationary and have positive and negative charges, while ions are taken dynamic and warm, and hot nonthermal electrons are assumed to be inertialess and kappa distributed in a dusty plasma. The Krylov–Bogoliubov–Mitropolsky method is used to derive the nonlinear Schrodinger equation (NLSE) for nonlinear amplitude modulation of dust-ion acoustic wave (DIAW) in plasmas. The dispersive and nonlinear coefficients of NLSE are obtained for DIAW, which depends on ion temperature, spectral indices of the nonthermal distributed electrons, dust density, and charge polarity of stationary dust particles. The modulationally stable and unstable regions of DIAW and its growth rate are investigated numerically. It is found that finite ion temperature, dust density, dust charge polarity, and spectral index of kappa for nonthermal electrons play a significant role to unstable the modulated DIAW modulated wave. The existence of positively and negatively charged dust particles and their observation in different regions of space plasma and in laboratory experiments is also pointed out.

Solitons in a generalized space- and time-variable coefficients nonlinear Schrödinger equation with higher-order terms

Abstract We introduce an approach that combines a similarity method with several transformations to find analytical solitary wave solutions for a generalized space- and time-variable coefficients of nonlinear Schrodinger equation with higher-order terms with consideration of varying dispersion, higher nonlinearities, gain/loss and external potential. One of these transformations is constructed in such a way that allows study of the width of localized solutions. Solitary-like wave solutions for front, bright and dark are given. The precise expressions of the solitonʼs width, peak, and the trajectory of its mass center and the external potential which are symbol of dynamic behavior of these solutions, are investigated analytically. In addition, the dynamical behavior of moving, periodic, quasi-periodic of breathing, and resonant are discussed. Stability of the obtained solutions is analyzed both analytically and numerically.

Nonlinear analysis and solitary waves for two superposed streaming electrified fluids of uniform depths with rigid boundaries

The nonlinear modulation of the interfacial waves of two superposed dielectric fluids with uniform depths and rigid horizontal boundaries, under the influence of constant normal electric fields and uniform horizontal velocities, is investigated using the multiple-time scales method. It is found that the behavior of small perturbations superimposed on traveling wave trains can be described by a nonlinear Schrodinger equation in a frame of reference moving with the group velocity. Wave-like solutions to this equation are examined, and different types of localized excitations (envelope solitary waves) are shown to exist. It is shown that when these perturbations are neutrally stable and sufficiently long, solutions to the nonlinear Schrodinger equation may be approximated by the well-known Korteweg-de Vries equation. The speed of the solitary on the interface is seen to be reduced by the electric field. It is found that there are two critical values of the applied voltage that lead to (i) breaking up of the solitary waves, and (ii) bifurcation of solutions of the governing equations. On the other hand, the complex amplitude of standing wave trains near the marginal state is governed by a similar type of nonlinear Schrodinger equation in which the roles of time and space are interchanged. This equation, under a suitable transformation, is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equations admit a solitary wave type of solutions with variable speed. Using the tangent hyperbolic method, it is observed that the wave speed increases as well as decreases, with the increase of electric field values, according to the chosen wavenumbers range. Finally, the nonlinear stability analysis is discussed in view of the coefficients of nonlinear Schrodinger equation to show the effects of various physical parameters, and also to recover the some limiting cases studied earlier in the literature.