Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics

In this work two kinds of smooth (compactons or cnoidal waves and solitons) and nonsmooth (peakons) solutions to the general Degasperis-Procesi (gDP) equation and its family (Degasperis-Procesi (DP) equation, modified DP equation, Camassa-Holm (CH) equation, modified CH equation, Benjamin-Bona-Mahony (BBM) equation, etc.) are reported in detail using different techniques. The single and periodic peakons are investigated by studying the stability analysis of the gDP equation. The novel compacton solutions to the equations under consideration are derived in the form of Weierstrass elliptic function. Also, the periodicity of these solutions is obtained. The cnoidal wave solutions are obtained in the form of Jacobi elliptic functions. Moreover, both soliton and trigonometric solutions are covered as a special case for the cnoidal wave solutions. Finally, a new form for the peakon solution is derived in details. As an application to this study, the fluid basic equations of a collisionless unmagnetized non-Maxwellian plasma is reduced to the equation under consideration for studying several nonlinear structures in the plasma model.

Simulation study on nonlinear structures in nonlinear dispersive media

In this work, the dynamic mechanism scenario of nonlinear electrostatic structures (unmodulated and modulated waves) that can propagate in multi-ion plasmas with the mixture of sulfur hexafluoride and argon gas is reported. For this purpose, the fluid equations of the multi-ion plasma species are reduced to the evolution (nonplanar Gardner) equation using the reductive perturbation technique. Until now, it has been known that the solution of nonplanar Gardner equation is not possible and for stimulating our data, it will solve numerically. At that point, the present study is divided into two parts: the first one is analyzing planar and nonplanar Gardner equations using the Adomian decomposition method (ADM) for investigating the unmodulated structures such as solitary waves. Moreover, a comparison between the analytical and numerical simulation solutions for the planar Gardner equation is examined, showing how powerful the ADM is in finding solutions in the short domain as well as its fast convergence, i.e., the approximate solution is consistent with the analytical solution for the planar Gardner equation after a few iterations. Second, the modulated envelope structures such as freak waves (FWs) are investigated in the framework of the Gardner equation by transforming this equation to the nonlinear Schrödinger equation (NLSE). Again, the ADM is used to solve the NLSE for studying FWs numerically. Furthermore, the effect of physical parameters of the plasma environment (e.g., Ar⁺-SF₅ ⁺-F^--SF₅ ^- plasma) on the characteristics of the nonlinear pulse profile is elaborated. These results help in a better understanding of the fundamental mechanisms of fluid physics governing the plasma processes.

Three dimensional ion-acoustic rogons in quantized anisotropic magnetoplasmas with trapped/untrapped electrons

Three-dimensional (3D) modulational instability (MI) and ion-acoustic (IA) envelopes are studied in a quantized degenerate magnetoplasma, whose constituents are the trapped/untrapped electrons and anisotropic positive ions. By using quantum hydrodynamic equations and the multiscale reductive perturbation technique, a 3D nonlinear Schrödinger equation is derived to account for electron quantization and ion pressure anisotrophy effects. The potential excitations are shown stable (unstable) against the perturbations for K_c<0(K_c>0), where K_c is a critical parameter that accounts for the longitudinal (transverse) dispersion(s) and nonlinearity effects. Numerically, the nonlinear evolution of IA wavepackets into a 3D MI may be revealed in the ranges of low and high frequencies 0<ω≤0.05 and 0.75≤ω≤1.1. The quantizing magnetic field reduces (enhances) the group speed (wave frequency) of IA excitations, concentrating the wave energy to favor the modulational instability. Finite electronic temperature (viz.,T_e≤10keV) enhances the untrapped electrons and significantly widens the instability domain K_c>0. The ionic pressure anisotropy increases the wave frequency (ω), piles up the harmonics under K_c>0, and give rise to modulational instability. The quantized magnetic field and anisotropic pressure reduce the amplitude and spatial extension of the IA rogons. This study is important for understanding the 3D MI and unstable excitations in degenerate plasmas, relevant to white dwarfs, neutron stars, and high-energy density experiments, where strong magnetic field quantizes the dynamics of trapped/untrapped electrons.

Large amplitude solitary waves in a warm magnetoplasma with kappa distributed electrons

The large amplitude nonlinear ion acoustic solitary wave propagating obliquely to an external magnetic field in a magnetized plasma with kappa distributed electrons and warm ions is investigated through deriving energy-balance-like expression involving a Sagdeev potential. Analytical and numerical calculations of the values of Mach number reveal that both of subsonic and supersonic electrostatic solitary structures can exist in this system. The influence on the soliton characteristics of relevant physical parameters such as the Mach number, the superthermal parameter, the directional cosine, the ratio of ion-to-electron temperature, and the ion gyrofrequency has been investigated.