An open problem on supernonlinear waves in a two-component Maxwellian plasma
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An open problem on supernonlinear waves in a two-component Maxwellian plasma Asit Saha1,a , Prasanta Chatterjee2,b , Santo Banerjee3,c 1 Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar,
Rangpo, East-Sikkim 737136, India
2 Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan 731235, India 3 Department of Mathematical Sciences, “Giuseppe Luigi Lagrange” Politecnico di Torino, Corso Duca degli
Abruzzi 24, Turin, Italy Received: 13 July 2020 / Accepted: 28 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract An unsolved problem in Maxwellian plasmas is delineated as, supernonlinear waves (SNWs) cannot exist in Maxwellian plasmas with less than three components. The criteria to generate SNWs in plasmas are the occurrence of at least two minima separated by at least one maxima in the curve of corresponding potential energy. This research is about the existence of SNWs in a two-component electron-ion plasma with Maxwell distributed electrons. The possible range of Mach number on the existence of SNWs is also reported. Analytical forms of all possible solitary, solitary-cusp and supernonlinear periodic wave solutions are derived. This research lights the existence of SNWs in a two-component Maxwellian plasma, which was unsolved till its inception from 2011.
1 Introduction Recently, a finite jump [1] between the amplitudes of solitary wave was reported depending on Mach number. But, the authors [1] were unable to classify the pattern of newly type solitary wave which was different from nonlinear solitary wave. Such new types of waves, called SNWS which are distinguished by nontrivial topology of the phase plots, were classified by Dubinov et al. [2] for the first time in plasmas. Topology of such a phase plot is not unique. Each trajectory of such a phase plot of the dynamical system refers to a nonlinear wave in plasma. If a close trajectory covers a separatrix layer in a phase plot of a dynamical system, then it is called a supernonlinear periodic wave. The generalized potential energy of a supernonlinear wave has at least two minima and at least one maxima separating the two minima. The minima and maxima of such potential correspond to centre and saddle point of the dynamical system, respectively. The occurrence of various minima and maxima of the potential energy is a dependable symptom that a supernonlinear wave can exist in the system. Ion-acoustic solitons were also reported experimentally in SF6-Ar plasma and laboratory experiment with chemically active plasmas [3,4].
a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] (corresponding author)
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Arbitrary amplitude ion-acoustic solitary wave with full nonlinearity was reported by Sagdeev [5] for the first time in plasmas. The technique [5] proposed by Sagdeev is known as Sagdeev’
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