Types Of Solitary Waves Research Articles

Nonlinear quantum ion acoustic waves in a Fermi plasma

Ion acoustic waves in a homogeneous quantum plasma, comprising of positive, negative ions, and electrons, have been investigated via the Korteweg–de Vries equation. The positive and negative ions are taken inertial and electrons are taken as inertialess. It is determined that the dispersive property of quantum plasma is strongly related to the quantum diffraction parameter. The quantum diffraction parameter (He), ion mass ratio (m), and negative ion temperature ratio (β) blatantly influence the propagation and type (compressive/rarefactive) of nonlinear ion acoustic solitary wave. It is noticed that soliton amplitude follows a dual trend at higher and lower concentrations of negative ions. The theoretical calculations presented are applicable to analyze the propagation of ion acoustic waves in a quantum electron-ion plasma containing negative ions in addition.

Problem of heavy fluid flow above a plate in the presence of a vortex

The free-surface flow of a heavy incompressible inviscid ideal fluid along a semi-infinite plate with the formation of a vortex near its edge is investigated. Solitary wave type flows are considered. A unique solution with a free vortex is obtained.

Convex and concave types of second baroclinic mode internal solitary waves

Abstract. Two types of second baroclinic mode (mode-2) internal solitary waves (ISWs) were found on the continental slope of the northern South China Sea. The convex waveform displaced the thermal structure upward in the upper layer and downward in the lower layer, causing a bulge in the thermocline. The concave waveform did the opposite, causing a constriction. A few concave waves were observed in the South China Sea, marking the first documentation of such waves. On the basis of the Korteweg-de Vries (K-dV) equation, an analytical three-layer ocean model was used to study the characteristics of the two mode-2 ISW types. The analytical solution was primarily a function of the thickness of each layer and the density difference between the layers. Middle-layer thickness plays a key role in the resulting mode-2 ISW. A convex wave was generated when the middle-layer thickness was relatively thinner than the upper and lower layers, whereas only a concave wave could be produced when the middle-layer thickness was greater than half the water depth. In accordance with the K-dV equation, a positive and negative quadratic nonlinearity coefficient, α2, which is primarily dominated by the middle-layer thickness, resulted in convex and concave waves, respectively. The analytical solution showed that the wave propagation of a convex (concave) wave has the same direction as the current velocity in the middle (upper or lower) layer. Analysis of the three-layer ocean model properly reproduced the characteristics of the observed mode-2 ISWs in the South China Sea and provided a criterion for the existence of convex or concave waves. Concave waves were seldom seen because of the rarity of a stratified ocean with a thick middle layer. This analytical result agreed well with the observations.

Theory for a dissipative droplet soliton excited by a spin torque nanocontact

A distinct type of solitary wave is predicted to form in spin torque oscillators when the free layer has a sufficiently large perpendicular anisotropy. In this structure, which is a dissipative version of the conservative droplet soliton originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the damping that would otherwise destroy the mode. Asymptotic methods are used to derive conditions on perpendicular anisotropy strength and applied current under which a dissipative droplet can be nucleated and sustained. Numerical methods are used to confirm the stability of the droplet against various perturbations that are likely in experiments, including tilting of the applied field, nonzero spin torque asymmetry, and nontrivial Oersted fields. Under certain conditions, the droplet experiences a drift instability in which it propagates away from the nanocontact and is then destroyed by damping.

Linear and nonlinear quantum ion acoustic waves in a plasma with positive, negative ions and Fermi electron gas

Linear and nonlinear propagations of quantum ion acoustic waves in positive, negative ions and electron plasma have been vetted via the dispersion relation and Korteweg–de Vries equation, where the ions are inertial and electrons are inertialess. The quantum mechanical effects arising due to the quantum diffraction and Fermi–Dirac statistics for this system are taken into account. The existence, as well as the type (compressive/rarefactive) of solitary wave propagating in the system, is strongly dependent on the numerical value of dimensionless quantum parameter He. It is observed that negative ion population and ion mass ratio have emphatic influence on the phase velocity of ion acoustic wave and the propagation of localized coherent solitary structures at quantum scale in the system.

Nonlinear acoustic waves in nonthermal dusty or pair plasmas

Using a Sagdeev pseudopotential formalism where nonlinear structures are stationary in a comoving frame, large dust-acoustic solitary waves and double layers have been studied in plasmas with negative cold dust or heavier ions, in the presence of nonthermal electrons and protons/positrons. The existence domain of negative solitary waves is limited by infinite compression of the negative dust or heavy ion species, that of positive solitary waves by the occurrence of positive double layers. These double layers require a sufficient degree of nonthermality of the hot species. There are parameter ranges where both negative and positive solitary structures can occur; sometimes both of the solitary wave type or sometimes one solitary wave and the other a double layer. Great emphasis is placed on the determination of the existence domains in compositional parameter space, with the help of strong analytical results, before typical Sagdeev pseudopotentials and solitary wave profiles are presented. Subject to simple adjustments, these results apply equally to a conjugate plasma model of positive dust or heavy ions, together with nonthermal electrons and protons/positrons.

Characterization and stability of localized bulging/necking in inflated membrane tubes

We consider localised bulging/necking in an inflated hyperelastic membrane tube with closed ends. We first show that the initiation pressure for the onset of localised bulging is simply the limiting pressure in uniform inflation when the axial force is held fixed. We then demonstrate analytically how, as inflation continues, the initial bulge grows continually in diameter until it reaches a critical size and then propagates in both directions. The bulging solution before propagation starts is of the solitary-wave type, whereas the propagating bulging solution is of the kink-wave type. The stability, with respect to axially symmetric perturbations, of both the solitary-wave type and the kink-wave type solutions is studied by computing the Evans function using the compound matrix method. It is found that when the inflation is pressure-controlled, the Evans function has a single non-negative real root and this root tends to zero only when the initiation pressure or the propagation pressure is approached. Thus, the kink-wave type solution is probably stable but the solitary-wave type solution is definitely unstable.

Solitary wave solutions for a generalized KdV–mKdV equation with variable coefficients

In this work, a generalized time-dependent variable coefficients combined KdV–mKdV (Gardner) equation arising in plasma physics and ocean dynamics is studied. By means of three amplitude ansatz that possess modified forms to those proposed by Wazwaz in 2007, we have obtained the bell type solitary waves, kink type solitary waves, and combined type solitary waves solutions for the considered model. Importantly, the results show that there exist combined solitary wave solutions in inhomogeneous KdV-typed systems, after proving their existence in the nonlinear Schrödinger systems. It should be noted that, the characteristics of the obtained solitary wave solutions have been expressed in terms of the time-dependent coefficients. Moreover, we give the formation conditions of the obtained solutions for the considered KdV–mKdV equation with variable coefficients.

Nonlinear electrostatic waves in inhomogeneous dense dusty magnetoplasmas

The nonlinear electrostatic drift waves are studied using quantum hydrodynamic model in dusty quantum magnetoplasmas. The dissipative effects due to collisions between ions and dust particles have also been taken into account. The Korteweg–de Vries Burgers (KdVB) like equation is derived and analytical solution is obtained using tanh method. The limiting cases of KdV type solitary waves, Burger type monotonic shock waves and oscillatory shock solutions are also presented. It is found that both hump and dip type solitary structures are possible in quantum dusty plasmas. However, amplitude and width of the nonlinear structure depend on the dust charge polarity and its concentration in electron–ion quantum plasmas. The monotonic shock like structure is independent of the quantum parameter. It is found that shock strength is increased in the presence of positively charged particles in comparison with negatively charged dust particles. The oscillatory shock structures are also obtained and it is found that change in dust charge polarity only shifts the phase of the oscillatory shock in plasmas. The numerical results are also presented for illustration.

An integral description of the propagation of steady-state perturbations of the heavy liquid surface

The system of equations of motion describing the gravity wave propagation in a perfect heavy liquid layer is transformed into a new integral equation for the free surface elevations. In the limit cases, this integral equation describes the linear and nonlinear periodic waves as well as the known types of solitary waves. In this case a dispersion equation arises because perturbations of the second and higher orders of smallness are neglected. The integral equation allows for the propagation of invariable surface perturbations of arbitrary forms if their spatial spectrum is concentrated near small wave numbers (compared to the inverse wave amplitude). Several examples of solutions are presented.

Peculiarities of periodic and aperiodic energy-exchange regimes in the cascade quasi-synchronous parametric frequency conversion

The domains of existence and peculiarities of exact analytic solutions of the problem of quasi-synchronous interaction of four plane collinear monochromatic waves — modes in a quadratically nonlinear medium during cascade frequency conversion are analysed. It is shown that the unusual types of multicomponent cnoidal and solitary soliton-like waves (of periodic and aperiodic energy-exchange regimes) are realised. Two of the four components of the latter are proportional to the real and imaginary parts of the well-known Lorentzian dependence, which is commonly used to describe the dispersion of contributions from resonance transitions to the complex permittivity in the case of homogeneous line broadening.

Identification of solitary-wave solutions as an inverse problem: Application to shapes with oscillatory tails

The propagation of stationary solitary waves on an infinite elastic rod on elastic foundation equation is considered. The asymptotic boundary conditions admit the trivial solution along with the solution of type of solitary wave, which is a bifurcation problem. The bifurcation is treated by prescribing the solution in the origin and introducing an unknown coefficient in the equation. Making use of the method of variational imbedding, the inverse problem for the coefficient identification is reformulated as a higher-order boundary value problem. The latter is solved by means of an iterative difference scheme, which is thoroughly validated. Solitary waves with oscillatory tails are obtained for different values of tension and linear restoring force. Special attention is devoted to the case with negative tension, when the solutions have oscillatory tails.

Stabilization of vortex-soliton beams in nematic liquid crystals

We study the interaction of two optical beams of different wavelengths (colors) in a nematic liquid crystal. We consider the case for which one component carries an optical vortex and the other component describes a localized beam. It is shown that a beam in one color can stabilize a vortex in the other color, the vortex being unstable in the absence of the second beam. We also show that the bright vortex can guide the beam in a stable manner, provided that the nonlocality is large enough. In this context we find that a different type of solitary wave (nematicon) instability can arise, one for which a ring structure develops at its peak. The results of approximate modulation solutions for the interaction between the vortex and the beam are found to be in good quantitative agreement with direct numerical simulations.

Propagation of dispersion–nonlinearity-managed solitons in an inhomogeneous erbium-doped fiber system

In this paper, a generalized nonlinear Schrödinger–Maxwell–Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Bäcklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed.

Nonlinear acoustic waves in nonthermal plasmas with negative and positive dust

Using a Sagdeev pseudopotential formalism where nonlinear structures are stationary in a co-moving frame, large dust-acoustic solitary waves and double layers have been studied in plasmas with negative and positive cold dust, in the presence of nonthermal electrons and ions. This has been done in a systematic way, to delimit the compositional parameter space in which such modes can be found. The existence domain of negative/positive solitary waves is limited by infinite compression of the negative/positive dust or by the occurrence of negative/positive double layers. These double layers require a sufficient nonthermality of the electrons/ions and the presence of enough positive/negative dust. There are parameter ranges where both negative and positive solitary structures coexist, sometimes both of the solitary wave type, sometimes one a solitary wave and the other a double layer. Typical Sagdeev pseudopotentials and solitary wave profiles have been presented.

Study of nonlinear ion- and electron-acoustic waves in multi-component space plasmas

Abstract. Large amplitude ion-acoustic and electron-acoustic waves in an unmagnetized multi-component plasma system consisting of cold background electrons and ions, a hot electron beam and a hot ion beam are studied using Sagdeev pseudo-potential technique. Three types of solitary waves, namely, slow ion-acoustic, ion-acoustic and electron-acoustic solitons are found provided the Mach numbers exceed the critical values. The slow ion-acoustic solitons have the smallest critical Mach numbers, whereas the electron-acoustic solitons have the largest critical Mach numbers. For the plasma parameters considered here, both type of ion-acoustic solitons have positive potential whereas the electron-acoustic solitons can have either positive or negative potential depending on the fractional number density of the cold electrons relative to that of the ions (or total electrons) number density. For a fixed Mach number, increases in the beam speeds of either hot electrons or hot ions can lead to reduction in the amplitudes of the ion-and electron-acoustic solitons. However, the presence of hot electron and hot ion beams have no effect on the amplitudes of slow ion-acoustic modes. Possible application of this model to the electrostatic solitary waves (ESWs) observed in the plasma sheet boundary layer is discussed.

Symmetry, full symmetry groups, and some exact solutions to a generalized Davey–Stewartson system

The Lie symmetry algebra of a generalized Davey–Stewartson (GDS) system is obtained. The general element of this algebra depends on eight arbitrary functions of time, which has a Kac–Moody–Virasoro loop algebra structure and is isomorphic to that of the standard integrable Davey–Stewartson equations under certain conditions imposed on parameters and arbitrary functions. Then based on the symmetry group direct method proposed by Lou and Ma [J. Phys. A 38, L129 (2005)] the full symmetry groups of the GDS system are obtained. From the full symmetry groups, both the Lie symmetry group and a group of discrete transformations can be obtained. Finally, some exact solutions involving sech-sech2-sech2 and tanh-tanh2-tanh2 type solitary wave solutions are presented by a generalized subequation expansion method.

Periodic Semifolded Solitary Waves for (2+1)-Dimensional Variable Coefficient Broer–Kaup System

Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the (2+1)-dimensional variable coefficient Broer–Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic.

Weakly dispersive hydraulic flows in a contraction – Nonlinear stability analysis

The nonlinear stability of steady weakly dispersive hydraulic solutions of the forced Korteweg de-Vries equation is investigated here. For numerical convenience the solutions are considered as periodic pairs consisting of an upward and downward jump. Two types of instability are found to occur. For largely symmetric problems, a solitary wave type instability dominates which features subexponential growth prior to saturation. For asymmetric solutions, the downward jump is destabilized by a hydraulic instability in which superexponential growth occurs prior to saturation. A qualitative description of both instability processes is presented using wave kinematics.

Nonlinear analysis and solitary waves for two superposed streaming electrified fluids of uniform depths with rigid boundaries

The nonlinear modulation of the interfacial waves of two superposed dielectric fluids with uniform depths and rigid horizontal boundaries, under the influence of constant normal electric fields and uniform horizontal velocities, is investigated using the multiple-time scales method. It is found that the behavior of small perturbations superimposed on traveling wave trains can be described by a nonlinear Schrodinger equation in a frame of reference moving with the group velocity. Wave-like solutions to this equation are examined, and different types of localized excitations (envelope solitary waves) are shown to exist. It is shown that when these perturbations are neutrally stable and sufficiently long, solutions to the nonlinear Schrodinger equation may be approximated by the well-known Korteweg-de Vries equation. The speed of the solitary on the interface is seen to be reduced by the electric field. It is found that there are two critical values of the applied voltage that lead to (i) breaking up of the solitary waves, and (ii) bifurcation of solutions of the governing equations. On the other hand, the complex amplitude of standing wave trains near the marginal state is governed by a similar type of nonlinear Schrodinger equation in which the roles of time and space are interchanged. This equation, under a suitable transformation, is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equations admit a solitary wave type of solutions with variable speed. Using the tangent hyperbolic method, it is observed that the wave speed increases as well as decreases, with the increase of electric field values, according to the chosen wavenumbers range. Finally, the nonlinear stability analysis is discussed in view of the coefficients of nonlinear Schrodinger equation to show the effects of various physical parameters, and also to recover the some limiting cases studied earlier in the literature.