Dust-acoustic envelope solitons in super-thermal plasmas

The modulational instability (MI) of the dust-acoustic waves (DAWs) in an electron-positron-ion-dust plasma (containing super-thermal electrons, positrons and ions along with negatively charged adiabatic dust grains) is investigated by the analysis of the nonlinear Schr\"{o}dinger equation (NLSE). To derive the NLSE, the reductive perturbation method has been employed. Two different parametric regions for stable and unstable DAWs are observed. The presence of super-thermal electrons, positrons and ions significantly modifies both the stable and unstable regions. The critical wave number $k_c$ (at which modulational instability sets in) depends on the super-thermal electron, positron, and ion, and adiabatic dust concentrations.Comment: 11 pages; 8 figure

Electrostatic rogue waves in double pair plasmas

A nonlinear Schr\"{o}dinger equation is derived to investigate the modulational instability (MI) of ion-acoustic (IA) waves (IAWs) in a double pair plasma system containing adiabatic positive and negative ion fluids along with super-thermal electrons and positrons. The analytical analysis predicts two types of modes, viz. fast ($\omega_f$) and slow ($\omega_s$) IA modes. The possible stable and unstable parametric regions for the IAWs in presence of external perturbation can be observed for both $\omega_f$ and $\omega_s$. The number density of the negative ions and positrons play a vital role in generating the IA rogue waves (IARWs) in the modulationally unstable region. The applications of our present work in astrophysical environments [viz. D-region ($\rm H^+, O_2^-$) and F-region ($\rm H^+, H^-$) of the Earth's ionosphere] as well as in laboratory plasmas [viz. pair-ion Fullerene ($\rm C^+, C^-$)] are pinpointed.Comment: 5 pages; 6 figure

Self-gravitating envelope solitons in a degenerate quantum plasma system

The existence and the basic features of ion-acoustic (IA) envelope solitons in a self-gravitating degenerate quantum plasma system (SG-DQPS), containing inertial non-relativistically degenerate light and heavy ion species as well as inertialess non-relativistically degenerate positron and electron species, have been theoretically investigated by deriving the nonlinear Schr\"{o}dinger (NLS) equation. The NLS equation, which governs the dynamics of the IA waves, has disclosed the modulationally stable and unstable regions for the IA waves. The unstable region allows to generate bright envelope solitons which are modulationaly stable. It is found that the stability and the growth rate dependent on the plasma parameters (like, mass and number density of the plasma species). The implications of our results in astronomical compact object (viz. white dwarfs, neutron stars, and black holes, etc.) are briefly discussed.Comment: 6 figures,6 page

Electrostatic acoustic modes in a self-gravitating complex plasma with variable charge impurities

A linear theory of dust acoustic (DA) and dust ion-acoustic (DIA) waves in a self-gravitating collisional dusty plasma contaminated by variable-charge impurities is presented for a self-consistent closed system. The ion-drag force arising from the ion orbital motion as well as momentum transfer from all the ions and self-gravitation are taken into consideration. The physical processes, viz., dust-charge relaxation, ionization, recombination and collisional dissipations are also taken into account self-consistently. The generalized dispersion relation describing the coupling of the acoustic modes with the dust-charge relaxation mode (CRM) and damping of the waves is derived and analyzed numerically.Comment: 13 pages, 5 figures. Physics Letters A (2005,To be published

Dust-acoustic rogue waves in four component plasmas

A theoretical investigation has been made on modulational instability (MI) and dust-acoustic (DA) rogue waves (DARWs) in a four dusty plasma medium containing inertial negatively charged massive heavy (light) cold (hot) dust grains as well as super-thermal electrons and non-thermal ions. The reductive perturbation method is used to derive the nonlinear Schr\"{o}dinger equation, and two types of modes, namely fast and slow DA modes, have been observed. The conditions for the MI and the formation of associated DARWs are found to be significantly modified by the effects of non-thermality of ions ($\alpha$), super-thermality of electrons ($\kappa$), density-ratio of non-thermal ion to cold dust ($\mu_i$), and mass-ratio of cold dust to hot dust ($\sigma$), etc. The implications of our current investigation in space and laboratory plasmas are briefly discussed.Comment: 5 figures; 5 page

Rogue waves in multi-pair plasma medium

The nonlinear propagation of ion-acoustic (IA) waves (IAWs), which are governed by the nonlinear Schr\"{o}dinger equation (NLSE), in multi-pair plasmas (MPPs) containing adiabatic positive and negative ion fluids as well as non-extensive ($q$-distributed) electrons and positrons, is theoretically investigated. It is observed that the MPP under consideration supports two types of modes (namely, fast and slow IA modes), and the modulationally stable and unstable parametric regimes for the fast and slow IA modes are determined by the sign of the ratio of the dispersive coefficient to the nonlinear one. It is also found that the modulationally unstable regime generates highly energetic IA rogue waves (IARWs), and the amplitude as well as the width of the IARWs decrease with increase in the value of $q$ (for both $q>0$ and $q<0$ limits). These new striking features of the IARWs are found to be applicable in the space [viz. D-region ($\rm H^+, O_2^-$) and F-region ($\rm H^+, H^-$) of the Earth's ionosphere] and laboratory MPPs [viz. fullerene ($\rm C^+, C^-$)].Comment: 8 figures, 5 page

Self-gravitating envelope solitons in astrophysical compact objects

The propagation of ion-acoustic waves (IAWs) in a collisionless unmagnetized self-gravitating degenerate quantum plasma system (SG-DQPS) has been studied theoretically for the first time. A nonlinear Schr\"{o}dinger equation is derived by using the reductive perturbation method to study the nonlinear dynamics of the IAWs in the SG-DQPS. It is found that for $k_c > k$ ($k_c < k$) (where $k_c$ is critical value of the propagation constant $k$ which determines the stable and unstable region of IAWs) the IAWs are modulationally unstable (stable), and that $k_c$ depends only on the ratio of the electron number density to light ion number density. It is also observed that the self-gravitating bright envelope solitons are modulationally stable. The results obtained from our present investigation are useful for understanding the nonlinear propagation of the IAWs in astrophysical compact objects like white dwarfs and neutron stars.Comment: 6 figure

On A New Form of Darboux-B\"acklund Transformation for DNLS Equation-Mixed and Rational Type Solutions

A new form of Darboux-B\"acklund transformation and its higher order form is derived for Derivative Nonlinear Schrodinger Equation(DNLS). The new form arises due to the different form of Lax pair. It is observed that by a special choice of the eigenvalue of DB transformation one can generate a mixed form of solution(containing both algebraic and exponential dependence on (x, t) can be generated. On the other hand by adopting a new methodology due to Neugebauer et. al. it is found that purely rational solution can be constructed. The two different approach yields different class of solution and are compared.Comment: 12 pages 8 figure

Solitary Optical pulse propagation in fused fibre coupler, Effect of Raman Scattering and switching

We analyse the motion of solitary type optical pulse in a fused optical fibre coupler when inter channel raman scattering (IRS) is taken into account and same type of dispersion management is used for both the core. The paper is divided into two sections . In the first half we utilise a moment method to study the variations of the different parameters of the Gaussian pulse, such as chirp, frequency, energy etc. while in the second half assuming a general form of the stationary pulse we discuss the switching phenomena due to the coupling. It is shown that lauching a pulse in one arm of the coupler can generate pulses in both the arms, but the patterns differs in a significant manner when the strength of IRS gets changedComment: 8 pages, 8 figures. Chaos, Solitons, Fractals (2005, to appear

On The Darboux B\"acklund Transformation of Optical Solitons with Resonant and Nonresonant Nonlinearity

Solitons in nonlinear optics holds a special role both in theoretical and experimental studies. Several types of evolution equations are seen to govern different situation of physical relevance. One such is the existence of both resonant and nonresonant situation in optical fibre. The corresponding evolution equation was devised by Doktorov et. al., which consists of a forced NLS equation along with two other equations for population difference and polarization. Here, we have followed an earlier formulation of Neugebauer for Darboux-B\"acklund transformation for this coupled systems. This formalism has the advantage that one can write the N-soliton solution altogether.An important difference with the usual non-linear system is that all the field variables are not present in both part of Lax operator. So we are to apply the DT to both part separately.Comment: 6 pages no figure