The modulational instability (MI) of ion-acoustic waves (IAWs) in a two-component plasma is investigated in the context of the nonextensive statistics proposed by Tsallis [J. Stat. Phys. 52, 479 (1988)]. Using the reductive perturbation method, the nonlinear Schrödinger equation (NLSE) which governs the MI of the IAWs is obtained. The presence of the nonextensive electron distribution is shown to influence the MI of the waves. Three different ranges of the nonextensive q-parameter are considered and in each case the MI sets in under different conditions. Furthermore, the effects of the q-parameter on the growth rate of MI are discussed in detail.

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A plasma channel produced by a short ionising laser pulse is axially nonuniform resulting from the self-defocusing. Through such preformed plasma channel, when a delayed pulse propagates, the phenomena of diffraction, refraction and self-phase modulation come into play. We have solved the nonlinear parabolic partial differential equation governing the propagation characteristics for an approximate analytical solution using variational approach. Results are compared with the theoretical model of Liu and Tripathi (Phys. Plasmas 1, 3100 (1994)) based on paraxial ray approximation. Particular emphasis is on both beam width and longitudinal phase delay which are crucial to many applications.

In the present investigation the modulational instability (MI) of dust acoustic wave (DAW) in four-component dusty plasma consisting of negative and positive charged dust grains and kappa (κ) distributed electrons and ions is studied. Considering the multifluid plasma model and using the reductive perturbation technique, nonlinear Schrödinger equation, which governs the MI of DAW, is obtained. It is found that presence of positive dust component, kappa-distributed electrons (κe), ions (κi), and temperature ratio (σ) significantly modify the domain of the MI and localized envelope excitations. Further, the effects of these parameters on the growth rate of MI have also been discussed in detail.

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In this research paper, the authors study the propagation of ion-acoustic solitons in a plasma consisting of warm positive and negative ions with different concentration of masses, charged states, and nonisothermal electrons. To account for the full nonlinearity of plasma equations, a quasipotential method is used here. The potential so obtained is characterized for solitons as a function of Mach number, positive and negative ions temperature, nonisothermal electrons, different concentration of negative and positive ions over a wide range of parameter space. Corresponding to isothermal case with β=1, coexistence of compressive and rarefactive solitons is obtained. For non-negative β≠1, only compressive solitons are observed. The prediction, that with introduction of negative ions there exists a critical ion concentration below which compressive solitons exist and above which rarefactive solitons exist, is ruled out for nonisothermal electrons.

This paper presents an investigation of the self-focusing of cosh-Gaussian laser beam in a plasma with linear absorption taking into account the combined effects of relativistic and ponderomotive type nonlinearities. Nonlinear parabolic partial differential equation governing the evolution of complex envelope in slowly varying envelope approximation is solved using variational approach. Self-focusing and self-phase modulation as well as self-trapping of cosh-Gaussian beam are studied at various values of decentered parameter b, with different absorption levels ki′. Numerical analysis shows that these parameters play vital role on propagation characteristics.