Solitonic, Periodic and Quasiperiodic Behaviors of Dust Ion Acoustic Waves in Superthermal Plasmas

Abstract

The solitonic, periodic, and quasiperiodic behaviors of dust ion acoustic waves in superthermal plasmas with q-nonextensive electrons are studied using the bifurcation theory of planar dynamical systems through direct approach. Using a Galilean transformation, model equations are transformed to a Hamiltonian system involving electrostatic potential. The existence of solitary and periodic waves is shown for the unperturbed Hamiltonian system. Analytical forms of these waves are presented depending on physical parameters q and μ. The effects of q and μ are studied on characteristics of nonlinear dust ion acoustic solitary and periodic waves. It is observed that parameters q and μ significantly influence the characteristics of nonlinear dust ion acoustic solitary and periodic structures. Considering an external periodic perturbation, the quasiperiodic behavior of the perturbed Hamiltonian system for dust ion acoustic waves is studied. It is seen that the unperturbed Hamiltonian system has the solitary and periodic wave solutions whereas the perturbed Hamiltonian system has quasiperiodic motion for same values of parameters q, μ and v.

Nonlinear dust-acoustic modes in homogeneous dusty plasmas: bifurcation analysis

“…where s is the constant and y F G , ( )is the fixed value along each solution curve. If the system is not Hamiltonian, then it doesn't have any closed orbits in the phase portrait and consequently there is neither solitary or periodic wave solutions [34,35]. The system (24) has three equilibrium points (critical points) are…”

“…This can be accessed using Melnikov theory [28][29][30]. Investigation of periodic solutions, solitonic structures, and chaotic structures [31][32][33][34] in dusty plasma dynamics is very a important role in solutions description. Consequently, different kind structures like periodic, solitonic, quasi-periodic, and chaotic behavior in nonlinear phenomenon plasma physics dynamics are remarkable area of plasma physics.…”

Higher‐order inertial Alfvén wave dressed solitons, quasiperiodic structures, and chaos in plasmas

“…During the last two decades, a lot of research work has been published on chaotic, periodic, and quasiperiodic on different plasma waves, which depends on the strength of the controlling parameters, external perturbations, and initial conditions [ 32–36 ] and references therein. Recently, the dynamical behaviour of arbitrary amplitude ion acoustic wave in a quantum plasma has been studied in the presence of pseudo external periodic force.…”

Bifurcation analysis of ion-acoustic waves in an adiabatic trapped electron and warm ion plasma

“…the solitary wave solution and periodic wave solution [23]. For instance, the nonlinear behaviour of dust ion acoustic (DIA) waves in a nonextensive plasma has been explored by Saha et al [24]. They have found that the effects of plasma parameters significantly alter the characteristics of nonlinear DIA solitary and periodic structures.…”