Macro-Experimental Observation of the Staggered Mode in Lattice System

The staggered mode of solitons in polyacetylene which is first discovered by Sun et al.is one of the typical gap soliton studied in lattice system.Using a one dimensional damped and parametrically driven pendulum lattice,we have observed a stable staggered mode which can be explained successfully by a nonlinear Schrödinger equation under the multiple scale approximation.

New Exact Solutions of the CDGSK Equation Related to a Non-local Symmetry

A non-local symmetry of the Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation has been used for finding exact solution in two different ways.Firstly,using the standard prolongation approach,we obtain the finite Lie Bäcklund transformation and the single soliton solution.Secondly,combining some local symmetries and the nonlocal symmetry,we get the group invariant solution which is described by the Weierstrass elliptic function and is deduced to the so-called interacting soliton for a special parameter.

Abundant Symmetry Structure of the Kaup-Kupershmidt Hierarchies

Explicit computation for the Kaup-Kupershmidt(KK)equation shows that there exists an abundant symmetry structure of the KK hierarchy.The recursion operator,inverse recursion operator and the symmetries all can be expressed explicitly by the pseudopotential of the KK equation.

THE MAPPING RELATION AMONG SOLUTION OF SOME NONLINEAR EQUATIONS

Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.

Nonlocal Lie-Backlund Symmetries and Olver Symmetries of the KdV Equation

Starting from a special nonlocal Lie Backlund symmetry of the KdV,mKdV,potential mKdV and singularity manifold equation system,three sets of higher order nonlocal Olver syiniuetries are reobtained.The soliton solutions of these models can also be obtained from the finite Lie-Backlund transformations.

New Symmetry Constraints of the Modified Kadomtsev-Petviashvili Equation

Using the inner parameter dependent symmetry constraints of the modified Kadomtsev-Petviashvili equation,we get an integrable(2+1)-dimensional multi-component Burgers and a(2+1)-dimensional integrable extensions of the derivative nonlinear Schrödinger equation.

GENERALIZATION TO CYLINDRICAL COORDINATE SYSTEM FOR THE HIGHER ORDER KDV AND KP EQUATION

Two new model equations which we call a higher order cylindrical KdV equation and a higher order cylindrical KP equation are proposed when we consider the 2-dimensional modulation of water waves with surface tension in cylindrical coordinate system.Some exact (2+1)-dimensional solitary wave solutions have been obtained by relating them to the higher order KdV equation through an appropriate variable transformation.

CYLINDRICAL ENVELOPE SOLITARY WAVES

The method of multiple-scales is used to investigate the nonlinear modulation of capillary-gravity waves with cylindrical symmetry.We find that the evolution of wave-packets is described by a nonlinear schrödinger-like equation i(U+U/2r)+αUξξ+β|U|2U=0.Some exact and explicit cylindrical envelope solitary wave solutions are also obtained by means of variable transformations.

Chaotic Behavior of Solitary Wave in Liquid

The chaotic behaviors of the time series of the breather(soliton)amplitude have been observed experimentally in the shallow water in the trough subjected to parametric exciting vertically.The results predict that the water solitary waves should be described by some chaotic equations in the higher order approximations as well as by the nonlinear Schördinger equation in the first order.

GENERALIZED BOUSSINESQ EQUATION AND KdV EQUATION——PAINLEVE PROPERTIES,BACKLUND TRANSFORMATIONS AND LAX PAIRS

Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coefficients. Using the singularity analysis methoddeveloped by J. Weiss and M. D. Kruskal et al. we have proved the sufficient conditionsof the integrabilities and Painleve properties of these two equations. Their Backlund trans-formations and the singularity manifold equations (generalized Schwartz-Boussinesq equationand Schwartz-KdV equation) are obtained. And then these two equations are linearized, i. e.their Lax pairs are given with the time-independent arbitrary spectral parameters includedexplicitly.

On two recurrence formulas for two kinds of identities of Riemann Zeta function

For any complex s, let ζ（s） denote Riemann Zeta function. We have ζ（s）=sum from n=1 to ∞ （1/ns） when Re（s）】1. Now we define A（n,k,l）=sum from α1+α2+……+αk=n to （（α1α2…αk）1ζ（2α1）ζ（2α2）…ζ（2αk））, where n≥k is a positive integer, α+α2+…αk=n denotes the summation for k-dimensional group of positive integers （α1, α2,…, αk）which satisfies this formula. In this note, our main purpose is to discuss computing problem of summation on equation （1）.

THE THEORETICAL CONSTRAINTS ON THE HIGGS-BOSON MASS AND THE WEINBERG ANGLE

The standard model describing the strong, the weak and the electromagnetic interactions has become the foundation of the modern physics. However, there still remain many important problems to be solved. The most important one is how to determine

Design of Quaternary ECL Q Gate

A new explanation of quaternary Q gate expression in Post algebra is given in this paper by using transmission function theory proposed in [1] and the quaternary ECL Q gate circuit is de- signed.The SPICE2 simulation to this circuit has confirmed that it has desired logical function and is totally compatible with various quaternary ECL circuits proposed before.

THE SUPPLEMENTARY RESEARCH IN TERNARY EDGE-TRIGGERED FLIP-FLOP

The usage of multiple-valued logic is not so common as binary logic in the electric science and technology. One reason is that it lacks the proper memory element which is not too complicated. Ref. [2] which studied the ternary masterslave flip-flop with three-rail output solved this problem. A sort of ternary edgetriggered D flip-flop corresponding to Ref. [2] has been designed in Ref. (3)

THE OPTIMIZED EXPANSION FOR SINE-GORDON FIELD THEORY AT ZERO AND FINITE TEMPERATURES IN D+1 DIMENSIONS

By means of the optimized expansion technique, the D + 1-dimensional quantum sine-Gordon (sG) field theory is studied nonperturbatively for both zero and finite temperatures.In 1 + 1 and 2+ 1 dimensions, the theory is finite when momentum cutoff Λ tends to infinity.The temperature-dependent Coleman phase transition conditions we obtained reduce to theknown results g_(cr)~2 =8π for 1+ 1 dimensions and g_(cr)~2= 16π/m_(RO) for 2+ 1 dimensions whenT→0. Especially, g_(cr) tends to zero at T→∞ limit both for 1 + 1 and 2 + 1 dimensions. Thereis no critical temperature making the Φ= 0 vacuum unstable. In 3 + 1 dimensions, if g^2 isfinite and Λ→∞, the theory is trivial. There is no nontrivial 'precarious' phase for the3+ 1-dimensional sG model. The effective potential for the 'autonomous' phase has asimilar form as the classical potential and the temperature effects only make contribution tothe infinitesimal part of this phase.