Cylindrical and spherical ion-acoustic envelope solitons in multicomponent plasmas with positrons

The nonlinear wave modulation of planar and nonplanar (cylindrical and spherical) ion-acoustic envelope solitons in a collisionless unmagnetized electron-positron-ion plasma with two-electron temperature distributions has been studied. The reductive perturbative technique is used to obtain a modified nonlinear Schrödinger equation, which includes a damping term that accounts for the geometrical effect. The critical wave number threshold Kc, which indicates where the modulational instability sets in, has been determined for various regimes. It is found that an increase in the positron concentration (α) leads to a decrease in the critical wave number (Kc) until α approaches certain value αc (critical positron concentration), then further increase in α beyond αc increases the value of Kc. Also, it is found that there is a modulation instability period for the cylindrical and spherical wave modulation, which does not exist in the one-dimensional case.