Using the two-channel Kohn and inverse Kohn variational methods, we investigate ground-state positronium (Ps) formation in positron-hydrogen collisions in the Ore gap. We find two zeros in the Ps-formation scattering amplitude f Ps and corresponding deep minima in the Ps-formation differential cross section, and we determine their positions accurately. Due to azimuthal symmetry, each zero in f Ps is part of separate circular rings of zeros for an azimuthal angle range of zero to 2π. We study the velocity field associated with f Ps in which we treat the magnitude of the momentum of the incident positron and the angle of the outgoing positronium as variables, and we refer to this velocity field as the extended velocity field. We show that it has two vortices that are connected with the zeros in f Ps , and that it rotates in opposite directions around the two zeros in f Ps . Previously, vortices in the velocity field associated with the transition matrix element have provided an explanation for deep minima in differential cross sections for direct ionization. With the introduction of the extended velocity field, our work shows that vortices can occur also for charge exchange.
Multi-soliton interaction of nonlinear ion sound waves in a pair-ion-electron (PIE) plasma having non-Maxwellian electrons including kappa, Cairns, and generalized two spectral index distribution functions are studied. To this end, a modified Korteweg-de Vries (mKdV) equation is obtained to investigate the ion-acoustic waves (IAWs) in a PIE plasma at a critical plasma composition. The effects of temperature and density ratios, and the non-Maxwellian electron velocity distributions on the overtaking interaction of solitons are explored in detail. The results reveal that both hump (positive peak) and dip (negative peak) solitons can propagate for the physical model under consideration. Two and three-soliton interactions are presented and the novel features of interacting compressive and rarefactive solitons are highlighted. The present investigation may be useful in laboratory plasmas where PIE plasmas have been reported.
In this article, we present a modified strategy that combines the residual power series method with the Laplace transformation and a novel iterative technique for generating a series solution to the fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use the Laurent series in their development. The new procedures’ advantages include the accuracy and speed in obtaining exact/approximate solutions. The suggested approach examines the fractional nonlinear BZ system that describes flow motion in a pipe.
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