Solitary Waves And Rogue Waves In The Plasma Models

Plasma is the quasi-neutral gas of charged and neutral particles which exhibits collective behaviour.They mainly exist in our cosmic space.The sun,accretion disk of black hole,comet tail,nebula,aurora,for instance,are composed by plasmas.Due to the presence of effects of long-ranged Coulomb force between the charged particles,and the anisotropy of the motions of these particles,there are abundant wave patterns(collective behaviors of the particles)in the plasmas.These wave patterns are closely associated with the phenomena in space physics and astrophysics,including the stellar evolution,solar flare,the effects of solar wind on the Earth's magnetosphere.Therefore,the investigations on the wave patterns in the plasmas are of important significance.In this thesis,we investigate the solitary waves and rogue waves in the plasmas by the numerical and analytical methods from the viewpoint of fluid mechanics.This thesis is composed by four parts.In the first part,we combine the variational iteration method and homotopy perturbation method and propose the variational homotopy perturbation iteration method which can be applied to fractional differential equation.We apply this method to the timefractional nonlinear differential equations appearing in the plasma physics(Under the sense of the modified Riemann-Liouville derivative).Via this method,we construct the approximate solutions of these equations.Moreover,we numerically simulate the nonlinear waves.In the second part,we investigate the dust-ion acoustic waves in a collisional onedimension plasma.Using the reductive perturbation method,a modified Kd V-Burgers equation is derived.The modified term are due to the collisional effect between the dust particles and ions.And we establish the numerical scheme using spectral method to solved the equation numerically.Also we prove the convergence of the numerical method.The numerical tests show the effectiveness of this method.In addition,we simulate the dust-ion solitary acoustic waves.Moreover,the effects of the plasmas parameter on the solitary wave are analyzed in detail.In the third part,we discuss amplitude modulation of planar and nonplanar onedimensional ion-acoustic waves in an unmagnetized electron-positron-ion-dust plasma.Via the reductive perturbation method,we derive a modified nonlinear Schr¨oinger(NLS)equation governing the envelope ion-acoustic waves.And we also investigate the modulation stability/instability of the waves.Here,the presence of modified term is due to the effect of nonplanar geometry and collision between the particles.For the plane case,we establish the numerical scheme via the spectral method to solve this equation.And we also analyze the properties of bright ion-acoustic solitary waves,which is due to the modulation instability.Furthermore,we study the first-and second-order rogue waves in the modulation instability region.Also how the plasma parameters influence the nonlinear structures of solitary waves and rogue waves is detailed discussed in this section.In the fourth part,we study the dust-acoustic waves in three-dimensional plasmas.We construct two plasma models in this section.The first unmagnetized plasma model consists of q-nonextensive electrons and ions,negatively charged dust grains,which is combined by the effects of bounded cylindrical geometry.A(3+1)-dimensional cylindrical Kd V is derived by the reductive perturbation method.And we propose the improved F-expansion method to construct some new solitary wave solutions of this equation.In the second model,we discuss the envelope dust-acoustic waves in a there-dimensional,magnetized plasma consisting of ?-distributed electrons,positive ions and negatively charged dust grains.The nonlinear propagation of envelope dust-acoustic waves is governed by(3+1)-dimensional nonlinear Schr¨oinger equation.Via the self-similarity transformation,we construct the first-and second-order rogue waves.And the effects of plasma parameters on the nonlinear waves in these two plasma models are detailed analyzed.