Effects of non-extensive electrons and positive/negative dust particles on modulational instability of dust-ion-acoustic solitary waves in non-planar geometry

Abstract

The nonlinear propagation of cylindrical and spherical dust-ion-acoustic (DIA) envelope solitary waves in unmagnetized dusty plasma consisting of dust particles with opposite polarity and non-extensive distribution of electron is investigated. By using the reductive perturbation method, the modified nonlinear Schrödinger (NLS) equation in cylindrical and spherical geometry is obtained. The modulational instability (MI) of DIA waves governed by the NLS equation is also presented. The effects of different ranges of the non-extensive parameter q on the MI are studied. The growth rate of the MI is also given for different values of q. It is found that the basic features of the DIA waves are significantly modified by non-extensive electron distribution, polarity of the net dust-charge number density and non-planar geometry.

Appendix

$$\begin{array}{@{}rcl@{}} B_{2\phi} &=& \frac{({-3k^{4}}/{\omega^{2}})+{\left( {1+\alpha s} \right)}C_{2}} {k^{2}-\omega^{2}[ {4k^{2}+{\left( {1+\alpha s}\right)}C_{2}}]},\\ B_{2u} &=&\frac{k}{\omega} B_{2\phi} +\frac{k^{3}}{2\omega^{2}},\\ B_{2n} &=&\frac{k}{\omega} B_{2u} +\frac{k^{4}}{\omega^{4}},\\ B_{0\phi} &=&\frac{2v_{\mathrm{g}} ({k^{3}}/{\omega^{3}})+v_{\mathrm{g}} ({k^{2}}/{\omega^{2}})-{v_{\mathrm{g}}^{2}}({1+\alpha s})C_{2}} {{v_{\mathrm{g}}^{2}} ({1+\alpha s})C_{1} -v_{\mathrm{g}}},\\ B_{0u} &=&\frac{1}{v_{\mathrm{g}}} \left[ {\left( {\frac{k}{\omega}}\right)^{2}+B_{0\phi}}\right],\\ B_{0n} &=&({1+\alpha s})C_{1} B_{0\phi} +2({1+\alpha s})C_{2}. \end{array} $$