GENERALIZED TRANSFER FUNCTION OF CONTROL SYSTEM AND AN IMPROVEMENT ON THE DECISION METHOD OF MOVEMENT STABILITY

In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.

New Jacobi Elliptic Function Solutions for the Generalized Nizhnik-Novikov-Veselov Equation

In this paper, a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the generalized Nizhnik-Novikov-Veselov equations are obtained. It is shown that the new method is much more powerful in finding new exact solutions to various kinds of nonlinear evolution equations in mathematical physics.

New useful special function in quantum optics theory

By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-l（x）y^m-l≡ n,m（x,y）.By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators（IWOP） we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.

Symplectic Schemes for Birkhoffian System

A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this paper the symplectic geometry structure of Birkhoffian system is discussed, then the symplecticity of Birkhoffian phase flow is presented. Based on these properties we give a way to construct symplectic schemes for Birkhoffian systems by using the generating function method.

New Explicit and Exact Solutions for the Klein-Gordon-Zakharov Equations

In this paper, based on the generalized Jacobi elliptic function expansion method, we obtain abundant new explicit and exact solutions of the Klein-Gordon- Zakharov equations, which degenerate to solitary wave solutions and triangle function solutions in the limit cases, showing that this new method is more powerful to seek exact solutions of nonlinear partial differential equations in mathematical physics.

Variational Description for the Generating Function Method of First Kind

We propose the variational description of generating function approach of first kind for Hamil-tonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any finite order accuracy scheme, and show that the resulting numerical scheme is multisymplectic. At last, we present some numerical experiments by using derived new scheme.

TWO NOVEL CLASSES OF ARBITRARY HIGH-ORDER STRUCTURE-PRESERVING ALGORITHMS FOR CANONICAL HAMILTONIAN SYSTEMS

In this paper,we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian systems.The one class is the symplectic scheme,which contains two new families of parameterized symplectic schemes that are derived by basing on the generating function method and the symmetric composition method,respectively.Each member in these schemes is symplectic for any fixed parameter.A more general form of generating functions is introduced,which generalizes the three classical generating functions that are widely used to construct symplectic algorithms.The other class is a novel family of energy and quadratic invariants preserving schemes,which is devised by adjusting the parameter in parameterized symplectic schemes to guarantee energy conservation at each time step.The existence of the solutions of these schemes is verified.Numerical experiments demonstrate the theoretical analysis and conservation of the proposed schemes.

Constructing Exact Solutions for Two Nonlinear Systems

Based on the computerized symbolic,a new generalized tanh functions method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (PDES)in a unified way.The main idea of our method is to take full advantage of an auxiliary ordinary differential equation which has more new solutions.At the same time,we present a more general transformation,which is a generalized method for finding more types of travelling wave solutions of nonlinear evolution equations(NLEEs).More new exact travelling wave solutions to two nonlinear systems are explicitly obtained.

Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.

On dynamical behavior for optical solitons sustained by the perturbed Chen–Lee–Liu model

This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber.The generalized exponential rational function method is used for this purpose.As a result,we obtain some non-trivial solutions such as the optical singular,periodic,hyperbolic,exponential,trigonometric soliton solutions.We aim to express the pulse propagation of the generated solutions,by taking specific values for the free parameters existed in the obtained solutions.The obtained results show that the generalized exponential rational function technique is applicable,simple and effective to get the solutions of nonlinear engineering and physical problems.Moreover,the acquired solutions display rich dynamical evolutions that are important in practical applications.