Higher Order Stability of Dust Ion Acoustic Solitary Wave Solution Described by the KP Equation

The lowest order stability of small amplitude dust ion acoustic solitary waves in a collisionless unmagnetized electron-positron-ion-dust plasma has been studied by Sardar et al. [Phys. Plasmas 23, 073703 (2016)]. Considering the weak dependence of the spatial coordinates perpendicular to the direction of wave propagation, they have obtained a Kadomtsev Petviashvili (KP) equation to study the lowest order stability of KdV (Korteweg-de Vries) soliton for long-wavelength plane-wave transverse perturbation with the help of small-k perturbation expansion approach of Rowlands and Infeld. In this paper, the lowest order stability analysis of KdV solitons discussed in the study by Sardar et al. [Phys. Plasmas 23, 073703 (2016)] has been extended up to a higher order using multiple-scale perturbation expansion approach of Allen and Rowlands [J. Plasma Phys. 50, 413 (1993); 53, 63 (1995)]. It has been found that the KdV soliton is stable at order \(k^{2}\) , where k denotes the wave number.