Soliton molecules and asymmetric solitons of the extended Lax equation via velocity resonance

We investigate the techniques for velocity resonance and apply them to construct soliton molecules using two solitons of the extended Lax equation.What is more,each soliton molecule can be transformed into an asymmetric soliton by changing the parameterφ.In addition,the collision between soliton molecules(or asymmetric soliton)and several soliton solutions is observed.Finally,some related pictures are presented.

The Extended Profiles of the Co-trees

The extended profile problem is to find a proper interval supergraph with the smallest possible number of edges.The problem stems from the storage and elimination techniques of a sparse symmetric matrix A in 1950,s.It has important applications in numerical algebra,VLSI designs and molecular biology.A tree T is a connected acyclic graph.The complement of a tree T is called a co-tree,denoted by Tˉ.In this paper the exact extended profile value of a cotree Tˉ is given.

Auto-Backlund Transformation and Extended Tanh-Function Methods to Solve the Time-Dependent Coefficients Calogero-Degasperis Equation

In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients.

Soliton, Positon and Negaton Solutions of Extended KdV Equation

Darboux transformation （DT） provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV （eKdV） equation, by which some new solutions such as singular soliton, negaton, and positon solutions are computed for the eKdV equation. We rediscover the soliton solution with finiteamplitude in [A.V. Slyunyaev and E.N. Pelinovskii, J. Exp. Theor. Phys. 89 （1999） 173] and discuss the difference between this soliton and the singular soliton. We clarify the relationship between the exact solutions of the eKdV equation and the spectral parameter. Moreover, the interactions of singular two solitons, positon and negaton, positon and soliton, and two positons are studied in detail.

Bifurcation Analysis and Bounded Optical Soliton Solutions of the Biswas-Arshed Model

We investigate the bounded travelling wave solutions of the Biswas-Arshed model(BAM)including the low group velocity dispersion and excluding the self-phase modulation.We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media.The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areaswhich correspond to different phase portraits.All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits.We also apply the extended sinh-Gordon equation expansion and the generalized Kudryashov integral schemes to obtain additional bounded optical soliton solutions of the BAM nonlinearity.We present more bounded optical shock waves,the bright-dark solitary wave,and optical rogue waves for the structure model via these schemes in different aspects.

The Theory of the Extended Electron (Anti-Particles of Dirac and Majorana)

This theory proposes an extended model of the electron based on the image of the screened electron in the concept of vacuum polarization of QED. The extended electron consists of a negatively charged core −q0which is surrounded by an assembly (an aggregation) of tiny static electric dipoles −q,+q. When subjected to an external field, electromagnetic forces are produced on these point charges to give rise to various properties of the electron. Three major properties of the electron that will be explored in this theory are: 1) the effective electric charge of the electron;2) the mechanism of the spin of the electron;3) the mechanism of radiation of the electron. The investigation of these properties leads to various innovative explanations for the generation of anti-particle, the orbital of the electron, the strong nuclear forces between nucleons … Other topics are also listed in the following content.

The Perturbation Bound of the Extended Vertical Linear Complementarity Problem

In this paper,we discuss the perturbation analysis of the extended vertical linear complementarity problem(EVLCP).Under the assumption of the row W-property,we derive several absolute and relative perturbation bounds of EVLCP,which extend some existing results.Several numerical examples are given to show the proposed bounds.

V-uniform ergodicity for fluid queues

In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.

Bright, periodic, compacton and bell-shape soliton solutions of the extended QZK and (3+1)-dimensional ZK equations

The(3+1)-dimensional Zakharov–Kuznetsov(ZK) and the new extended quantum ZK equations are functional to decipher the dense quantum plasma, ion-acoustic waves, electron thermal energy,ion plasma, quantum acoustic waves, and quantum Langmuir waves. The enhanced modified simple equation(EMSE) method is a substantial approach to determine competent solutions and in this article, we have constructed standard, illustrative, rich structured and further comprehensive soliton solutions via this method. The solutions are ascertained as the integration of exponential, hyperbolic,trigonometric and rational functions and formulate the bright solitons, periodic, compacton, bellshape, parabolic shape, singular periodic, plane shape and some new type of solitons. It is worth noting that the wave profile varies as the physical and subsidiary parameters change. The standard and advanced soliton solutions may be useful to assist in describing the physical phenomena previously mentioned. To open out the inward structure of the tangible incidents, we have portrayed the three-dimensional, contour plot, and two-dimensional graphs for different parametric values. The attained results demonstrate the EMSE technique for extracting soliton solutions to nonlinear evolution equations is efficient, compatible and reliable in nonlinear science and engineering.

Conversion from whispered speech to normal speech using the extended bilinear transformation method

A method of conversion from whispered speech to normal speech using the extended bilinear transformation was proposed. On account of the different deviation degrees of the whisper＇s formants in different frequency bands, the spectrum of the whispered speech will be processed in the separate partitions of this paper. On the basis of this spectrum, we will establish a conversion function able to usefully convert whispered speech to normal speech. Because of the whisper＇s non-linear offset in relation to normal speech, this paper introduces an expansion factor in the bilinear transform function making it correspond more closely to the actual conversion demands of whispered speech to normal speech. The introduction of this factor takes the non-linear move of the spectrum and the compression of the formant bandwidth into consideration, thus effectively reducing the spectrum distortion distance in the conversion. The experiment results show that the conversion presented in this paper effectively improves both the sound quality and the intelligibility of whispered speech.

Mixing via the extended family

In this paper,the relationship between the extended family and several mixing properties in measuretheoretical dynamical systems is investigated.The extended family eF related to a given family F can be regarded as the collection of all sets obtained as"piecewise shifted"members of F.For a measure preserving transformation T on a Lebesgue space(X,B,μ),the sets of"accurate intersections of order k"defined below are studied,Nε(A0,A1,...,Ak)=n∈Z+:μk i=0T inAiμ(A0)μ(A1)μ(Ak)<ε,for k∈N,A0,A1,...,Ak∈B and ε>0.It is shown that if T is weakly mixing(mildly mixing)then for any k∈N,all the sets Nε(A0,A1,...,Ak)have Banach density 1(are in(eFip),i.e.,the dual of the extended family related to IP-sets).

Recent advances in the extended finite element method (XFEM) and isogeometric analysis (IGA)

The finite element method （FEM） is one of the most popular and efficient methods for computational modeling in scien- tific research and engineering . To expand its application to more complex problems, lots of new FEM-based methods have been developed in recent decades.

An extensive analytical and numerical study of the generalized q-deformed Sinh-Gordon equation

In this paper,the q-deformed Sinh-Gordon equation is solved analytically using a new general form based on the extended tanh approach.The numerical solutions of the equation is obtained using a b-spline finite element method.Also,we present numerous figures to demonstrate the various solitons propagation patterns.This type of equation has not been previously dealt with in such ways,whether analytical or numerical.This study is very useful in studying several physical systems that have lost their symmetry.

The phase shift analysis of the colliding dissipative KdV solitons

In this work,the head-on collisions of the non-stationary dissipative soliton in ultracold neutral plasmas(UNPs)are investigated.The extended Poincare-Lighthill-Kuo(PLK)approach is adopted for reducing the fluid equations of the UNPs to two-counterpropagating damped Korteweg-de Vries(dKdV)equations.The dKdV equation is not an integrable Hamiltonian system,i.e.,does not have an exact solution.Thus,one of the main goal of this paper is to find a new general approximate analytical solution to the dKdV equation for investigating the mechanism of the propagation and interaction of the non-stationary dissipative solitons.The residual error is estimated for checking the accuracy of the new obtained solution.The approximate analytical soliton solutions are adopted for deriving the temporal phase shifts after the collision.The impact of physical parameters on the nonstationary dissipative soliton profile and the temporal phase shifts is discussed.The obtained results will contribute to understand the mechanism of propagation and interaction of many nonlinear phenomena in different nonlinear mediums such as ocean,sea,optical fiber,plasma physics,etc.

NUMERICAL ANALYSIS OF BIFURCATION PROBLEM WITH CORANK-n

In this paper, numerical approximation of solution branches of bifurcation problem with corank-n is studied.