Nonlinear cnoidal waves and solitary structures in unmagnetized plasmas with generalized (r, q) distributed electrons

Abstract

Theoretical investigation of electrostatic ion acoustic periodic (cnoidal) waves and solitons with warm ions is presented with electrons that are assumed to follow the double spectral index distribution function. The double spectral index distribution imitates effectively the distributions that have often been seen in space plasmas. Using the standard reductive perturbation technique, the Korteweg–de Vries (KdV) equation is derived which describes the nonlinear periodic waves with appropriate boundary conditions. By using planar dynamical system to this KdV equation, the existence of solitary wave solutions and periodic wave solutions are found. It is shown that changing the electron population in regions of low and high phase space density regions alter the propagation characteristics of nonlinear ion acoustic periodic and solitary structures. Comparison of non-Maxwellian distribution functions with Maxwellian distribution is also made. The importance of the present work with regard to space plasmas is also pointed out.

A new reductive perturbation formalism for ion acoustic cnoidal waves

“…(2018), Ur-Rehman, Mahmood & Kaladze (2019), Ur-Rehman & Mahmood (2019), Ali et al. (2020), Tamang & Saha (2020) and Mehdipoor & Asri (2022). In addition, the authors used similar boundary conditions to those satisfied by solitons.…”

“…Unfortunately, more recent studies of cnoidal waves in plasmas have ignored these facts, where conservation of number density has been completely ignored. Examples of this can be found in Saini & Sethi (2016), Ur-Rehman, Mahmood & Hussain (2017), Tolba et al (2017), Singh et al (2018), Liu et al (2018), Farhadkiyaei & Dorranian (2018, Kaur et al (2018), Ur-Rehman, Mahmood & Kaladze (2019), , Ali et al (2020), Tamang & Saha (2020) and Mehdipoor & Asri (2022). In addition, the authors used similar boundary conditions to those satisfied by solitons.…”

Physical aspects of cnoidal waves in non-thermal electron-beam plasma systems

“…According to our best knowledge, the structure of periodic IA waves in a nonthermal plasma with the double spectral index distribution function, and in the presence of electron beam effects has not been studied so far. Very recently, Ali et al [59] reported the study on nonlinear cnoidal waves and solitary structures in an unmagnetized plasma with generalized (r q , ) distribution function for electrons. The existence of solitary and periodic waves in such plasma has been confirmed using cnoidal wave solution of the K-dV equation [59].…”

“…Very recently, Ali et al [59] reported the study on nonlinear cnoidal waves and solitary structures in an unmagnetized plasma with generalized (r q , ) distribution function for electrons. The existence of solitary and periodic waves in such plasma has been confirmed using cnoidal wave solution of the K-dV equation [59]. They showed that the properties of nonlinear IA periodic and solitary waves will be modified as the electron population in regions of low and high phase-space density regions alters.…”

Interaction of electron acoustic solitons in auroral region for an electron beam plasma system

“…The standard Korteweg de Vries (KdV) equation involves the quadratic nonlinearity and the balance between nonlinearity and dispersion gives emergence to the solitary wave. The literature is replete with the investigation of KdV equation in a variety of physical situations of interest (Korteweg and Vries, 1895;Kakutani et al, 1968;Jeffrey, 1973;Mamun et al, 1996;Ali et al, 2020). It is well known that in a multicomponent plasma, there is a certain critical range of plasma parameters for which the quadratic nonlinearity ceases to exist and one then needs to go to the higher order to obtain physically meaningful solutions.…”