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Generalized Schamel nonlinear Schrödinger dynamics of ion-acoustic wave packets in electronegative plasmas with trapped negative ions

Chérif Souleman Panguetna1,*, Conrad Bertrand Tabi2,†, Stéphanie Ganyou1,‡, and Timoléon Crépin Kofané1,2,§

  • *Contact author: cherifps@yahoo.fr
  • †Contact author: tabic@biust.ac.bw
  • ‡Contact author: stephanieganyou@gmail.com
  • §Contact author: kofanet@biust.ac.bw
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Phys. Rev. E 114, 045213 – Published 28 October, 2026

DOI: https://doi.org/10.1103/9x1y-tnll

Abstract

We investigate the amplitude modulation of ion-acoustic wave packets in an unmagnetized electronegative plasma composed of cold positive ions, Boltzmann electrons, and negative ions following a Schamel trapped-particle distribution. The trapped-particle description is relevant to weakly collisional electronegative plasmas supporting Bernstein–Greene–Kruskal (BGK)-type potential structures and ion-hole equilibria, where a fraction of the negative-ion population can become trapped in the self-consistent wave potential. Unlike conventional analytic closures (Boltzmann, Tsallis, κ-distributed, nonthermal), which we show can only produce a cubic envelope nonlinearity regardless of their parametrization, this nonanalytic trapped-particle response naturally yields a generalized Schamel nonlinear Schrödinger equation combining the familiar cubic term with a genuinely noninteger |Ψ|1/2Ψ contribution. Derived through both a long-wavelength (Gardner-Schamel) limit and the full modulated-wave-packet limit, the resulting dispersion, cubic, and fractional coefficients are obtained in closed form. Two results stand out. First, the maximum modulational growth rate depends nonmonotonically on the negative-ion concentration, exhibiting an interior optimum that maximizes the instability above a critical temperature ratio, and, near the long-wavelength threshold, a finite concentration window outside of which the instability vanishes entirely. Second, a split-step Fourier analysis shows that the trapped-ion population breaks the time-symmetry of the Peregrine and Akhmediev rogue-wave solutions, causing them to build up faster than they decay, a signature invisible in the peak amplitude alone. These results extend previous electronegative plasma models and provide testable predictions for nonlinear wave localization in plasmas containing trapped particles.

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Phys. Rev. E 114, 045213– Published 28 October, 2026
  • Received 30 June 2026
  • Revised 9 September 2026
  • Accepted 7 October 2026
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