On the solitonic structures of the cylindrical dust-acoustic and dust-ion-acoustic waves with symbolic computation

Dusty plasmas can support the dust-ion-acoustic and dust-acoustic modes, modelled by the cylindrical Korteweg–de Vries equation as proposed. In this Letter, we point out that there exist a couple of problems in the plasma-physics literature on the cylindrical Korteweg–de Vries equation, i.e., the claim of non-existence of exact analytic solutions and omission of varying ambient field, to which we provide our answers. With symbolic computation, we obtain a family of exact analytic, solitonic solutions, of which the previous solutions in plasma physics turn out to be the special cases. With figures, we work out some possibly observable effects for the future plasma experiments, featured by a solitonic pulse aboard the varying ambient field propagating with its varying velocity and amplitude.     

Rogue waves in baroclinic flows

We investigate an AB system, which can be used to describe marginally unstable baroclinic wave packets in a geophysical fluid. Using the generalized Darboux transformation, we obtain higher-order rogue wave solutions and analyze rogue wave propagation and interaction. We obtain bright rogue waves with one and two peaks. For the wave packet amplitude and the mean-flow correction resulting from the self-rectification of the nonlinear wave, the positions and values of the wave crests and troughs are expressed in terms of a parameter describing the state of the basic flow, in terms of a parameter responsible for the interaction of the wave packet and the mean flow, and in terms of the group velocity. We show that the interaction of the wave packet and mean flow and also the group velocity affect the propagation and interaction of the amplitude of the wave packet and the self-rectification of the nonlinear wave.     

Darboux transformation and explicit solutions for the integrable sixth-order KdV equation for nonlinear waves

Korteweg-de Vries (KdV)-type equations can describe some physical phenomena in fluids, nonlinear optics, quantum mechanics, plasmas, etc. In this paper, with the aid of symbolic computation, the integrable sixth-order KdV equation is investigated. Darboux transformation (DT) with an arbitrary parameter is presented. Explicit solutions are derived with the DT. Relevant properties are graphically illustrated, which might be helpful to understand some physical processes in fluids, plasmas, optics and quantum mechanics.     

Analytical solving of a deformed KdV equation

The celebrated Korteweg-de Vries (KdV) topics are of crucial significance in many fields of natural sciences. In this paper, a symbolic-computation-based method is applied to a perturbed form of the modified KdV equation, and one type of the analytic solutions is obtained. This work has been supported by the Out-standing Young Faculty Fellowship & the Research Grants for the Scholars Returning from Abroad, State Education Commission of China.     

Multi-solitonic solutions for the variable-coefficient variant Boussinesq model of the nonlinear water waves

For the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth of the water, we consider a variable-coefficient variant Boussinesq (vcvB) model with symbolic computation. We construct the connection between the vcvB model and a variable-coefficient Ablowitz-Kaup-Newell-Segur (vcAKNS) system under certain constraints. Using the N-fold Darboux transformation of the vcAKNS system, we present two sets of multi-solitonic solutions for the vcvB model, which are expressed in terms of the Vandermonde-like and double Wronskian determinants, respectively. Dynamics of those solutions are analyzed and graphically discussed, such as the parallel solitonic waves, shape-changing collision, head-on collision, fusion-fission behavior and elastic-fusion coupled interaction.     

Dynamics of bound vector solitons induced by stochastic perturbations: Soliton breakup and soliton switching

We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.     

Quintic time-dependent-coefficient derivative nonlinear Schrödinger equation in hydrodynamics or fiber optics: bilinear forms and dark/anti-dark/gray solitons

Nonlinear Dynamics - Studies on the water waves contribute to the design of the related industries, such as the marine and offshore engineering, while the media with the negative refractive index...     

Analytic localized solitonic excitations for the (2+1)-dimensional variable-coefficient breaking soliton model in fluids and plasmas

In this paper, via the Painlevé analysis and multi-linear variable separation, the (2+1)-dimensional variable-coefficient breaking soliton model in certain fluids and plasmas is investigated, with the B?cklund transformation and analytic solutions presented explicitly. With those solutions, four kinds of the localized solitonic excitations are obtained, as the multi-shock-lump, multi-instanton, saddle-type-multiple-ring-soliton, and single-loop- breather structures. Figures indicate that the shapes, velocities, and propagation paths of those four kinds are affected by the variable coefficients, yielding the dynamic features, elastic interactions, parallel propagations, and periodic propagation of the analytic bound localized solitonic excitations.     

火焰原子吸收光谱法测定深裂竹根七中的4种金属元素

测定深裂竹根七中Cu、Zn、Cr和Mo 4种金属元素的含量.采用空气-乙炔火焰原子吸收光谱法对深裂竹根七药用部位中Cu、Zn、Cr和Mo元素的含量进行测定.所建立的校准曲线相关系数r＞0.9990,精密度实验RSD分别为1.3％-2.8％,重复性实验RSD分别为2.2％-2.9％,加标回收率91.0％-109.0％;方法简便快速,结果准确可靠,可用于深裂竹根七中Cu、Zn、Cr和Mo元素的含量测定.