Existence and stability of alternative dust ion acoustic solitary wave solution of the combined MKP-KP equation in nonthermal plasma

Abstract

The aim of this paper is to extend the recent work of Sardar et al. [Phys. Plasmas 23, 073703 (2016)] on the stability of the small amplitude dust ion acoustic solitary wave in a collisionless unmagnetized nonthermal plasma in the presence of isothermal positrons. Sardar et al. [Phys. Plasmas 23, 073703 (2016)] have derived a KP (Kadomtsev Petviashvili) equation to study the stability of the dust ion acoustic solitary wave when the weak dependence of the spatial coordinates perpendicular to the direction of propagation of the wave is taken into account. They have also derived a modified KP (MKP) equation to investigate the stability of the dust ion acoustic solitary wave when the coefficient of the nonlinear term of the KP equation vanishes. When the coefficient of the nonlinear term of the KP equation is close to zero, a combined MKP-KP equation more efficiently describes the nonlinear behaviour of the dust ion acoustic wave. This equation is derived in the present paper. The alternative solitary wave solution of the combined MKP-KP equation having profile different from sech2 or sech is obtained. This alternative solitary wave solution of the combined MKP-KP equation is stable at the lowest order of the wave number. It is found that this alternative solitary wave solution of the combined MKP-KP equation and its lowest order stability analysis are exactly same as those of the solitary wave solution of the MKP equation when the coefficient of the nonlinear term of the KP equation tends to zero.