Dust ion acoustic solitons in a complex dusty plasma system with an adiabatic state

Abstract

In this theoretical work nonlinear behavior of dust ion acoustic solitary waves (SWs) has been investigated, and then the effect of the adiabatic change on them has been observed. The complex plasma system consists of inertial positive and negative ions, Maxwell's electrons, and positively and negatively charged stationary dust particles. The effects of dust polarity on the dust ion acoustic SWs have also been observed. Using the reductive perturbation method, we first derive K-dV equation which lets to analyze both the positive (bright) and negative (dark) solitons in a very limited region. After that mK-dV equation has been derived, and this let to analyze positive soliton for a large region, but cannot show the negative soliton. Finally, the Gardner equation has been derived employing the same method, through which we were able to analyze both the positive and negative solitons for a large region. It has been found that both the positive and negative solitons significantly depend on the mass number density, ion number density, and dust polarity in the adiabatic and isothermal system.

Effect of the nonlinear dispersive coefficient on time-dependent variable coefficient soliton solutions of the Kolmogorov-Petrovsky-Piskunov model arising in biological and chemical science

“…Additionally, when dealing with nonlinear evolution equations it is important to have a thorough understanding of the characteristics of the equation itself, as well as the potential solutions, in order to ensure accuracy and avoid unnecessary computational effort. There are some techniques used to solve NLEEs successfully, such as N-fold Darboux transformation [ 16 ], simplified Hirota's direct method [ 17 ], modified exponential rational function scheme [ 18 ], Simplest equation and New form of modified Kudrusov procedure [ 19 ], new generalized exponential rational function technique [ 20 ], amplitude ansatz method [ 21 ], Hirota bilinear forms with Hirota direct method [ 22 , 23 ], unified scheme [ 24 ], New modified simple equation technique [ 25 ], backlund transformations [ 26 ], backlund transformation from the riccati form of an inverse method [ 26 ], simple symbolic computation approach [ 27 ], generalized projective riccati equations method [ 28 ] Sardar sub-equation and the MK approaches [ 29 ] sine-cosine scheme [ 30 ], reductive perturbation method [ 31 ], enhanced modified simple equation technique [ 32 ], and so on. The motivation of this work is to explore the variable coefficient solitary wave solution of classical Kolmogorov–Petrovsky–Piskunov (KPP) models.…”