continuous limits for an integrable coupling of the kac van moerbeke hierarchy in this paper we present an integrable coupling of lattice hierarchy and its continuous limits by using lie algebra sl 4 by introducing a complex discrete spectral problem the integrable coupling of kac van moerbeke lattice hierarchy is derived it is shown that a new complex lattice spectral problem converges to the integrable coupling of discrete soliton equation hierarchy which has the integrable coupling system of mkdv hierarchy as a new kind of continuous limit

a new 4 dimensional implicit vector form loop algebra with arbitrary constants and the corresponding computing formula of constant γ in the variation identity abstract a new 4 dimensional implicit vector form loop algebra containing several arbitrary constants is presented and the corresponding computing formula of constant in the variation identity is obtained in this paper as an application a new liouville integrable hierarchy is gotten which can be reduced to dirac hierarchy nonlinear sch o inger equation nls m kdv equation and so on

constructing 2 1 dimensional nonlinear soliton equations with a generalized zero curvature equation the generalized zero curvature equation is presented which is an important tool to construct the 2 1 dimensional integrable soliton equation hierarchy a few of new 2 1 dimensional integrable soliton equation hierarchies are obtained through the generalized zero curvature equation

integrable counterparts of the d kaup newell soliton hierarchy two integrable counterparts of the d kaup newell soliton hierarchy are constructed from a matrix spectral problem associated with the three dimensional special orthogonal lie algebra so 3 r an application of the trace identity presents hamiltonian or quasi hamiltonian structures of the resulting counterpart soliton hierarchies thereby showing their liouville integrability i e the existence of infinitely many commuting symmetries and conserved densities the involved hamiltonian and quasi hamiltonian properties are shown by computer algebra systems

even unimodular 12 dimensional quadratic forms over q 5 abstract a complete list of all 12 dimensional even unimodular lattices over q 5 is given theta series are used to verify that the list of those with 2 vectors is complete it is proved that there is a unique lattice with no 2 vectors and the siegel mass formula gives the order of its automorphism group

nonlinear continuous integrable hamiltonian couplings based on a kind of special non semisimple lie algebras a scheme is presented for constructing nonlinear continuous integrable couplings variational identities over the corresponding loop algebras are used to furnish hamiltonian structures for the resulting continuous integrable couplings the application of the scheme is illustrated by an example of nonlinear continuous integrable hamiltonian couplings of the akns hierarchy of soliton equations

the multi component coupled burgers hierarchy of soliton equations and its multi component integrable couplings system with two arbitrary functions abstract a new loop algebra g m is constructed which is devoted to establishing an isospectral problem by making use of tu scheme the multi component coupled burgers hierarchy is obtained furthermore an expanding loop algebra f m of the loop algebra g m is presented it follows that the multi component integrable coupling system of the multi component coupled burgers hierarchy is worked out in general the method can be applied to other evolution equations hierarchies

a new loop algebra and a corresponding integrable hierarchy as well as its integrable coupling a type of new interesting loop algebra gm m 1 2 with a simple commutation operation just like that in the loop algebra a1 is constructed with the help of the loop algebra gm a new multicomponent integrable system m akns kn hierarchy is worked out as reduction cases the m akns hierarchy and m kn hierarchy are engendered respectively in addition the system 1 akns kn which is a reduced case of the m akns kn hierarchy above is a unified expressing integrable model of the akns hierarchy and the kn hierarchy obviously the m akns kn hierarchy is again a united expressing integrable model of the multicomponent akns hierarchy m akns and the multicomponent kn hierarchy m kn this article provides a simple method for obtaining multicomponent integrable hierarchies of soliton equations finally we work out an integrable coupling of the m akns kn hierarchy

constructing nonlinear discrete integrable hamiltonian couplings beginning with lax pairs from special non semisimple matrix lie algebras we establish a scheme for constructing nonlinear discrete integrable couplings discrete variational identities over the associated loop algebras are used to build hamiltonian structures for the resulting integrable couplings we illustrate the application of the scheme by means of an enlarged volterra spectral problem and present an example of nonlinear discrete integrable hamiltonian couplings for the volterra lattice equations

a generalized fractional kn equation hierarchy and its fractional hamiltonian structure a generalized hamiltonian structure of the fractional soliton equation hierarchy is presented by using differential forms and exterior derivatives of fractional orders we construct the generalized fractional trace identity through the riemann liouville fractional derivative an example of the fractional kn soliton equation hierarchy and hamiltonian structure is presented which is a new integrable hierarchy and possesses hamiltonian structure

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

noncommutative integrable coupling system of tc equation hierarchy a noncommutative version of the tc soliton equation hierarchy is presented which possesses the zero curvature representation then we show that noncommutative nc tc equation can be derived from the noncommutative anti self dual yang mills equation by reduction finally an integrable coupling system of the nc tc equation hierarchy is constructed by using of the enlarged lax pairs

classical poisson structures and r matrices from constrained flows we construct the classical poisson structures and r matrices for some finite dimensional integrable hamiltonian systems obtained by constraining the flows of soliton equations in a certain way this approach allows us to produce new kinds of classical dynamical yang baxter structures to illustrate this method we present the r matrices associated with the constrained flows of the kaup newell kdv wki and tg hierarchies all generated by a two dimensional eigenvalue problem some of the r matrices thus obtained depend only on the spectral parameters but others depend also on the dynamical variables for consistency they have to obey a classical yang baxter type equation possibly with dynamical extra terms

integrable evolution systems based on gerdjikov ivanov equations bi hamiltonian structure finite dimensional integrable systems and n fold darboux transformation a spectral problem and the associated gerdjikov ivanov gi hierarchy of nonlinear evolution equations is presented as a reduction the well known gi equation of derivative nonlinear schrodinger equations is obtained it is shown that the gi hierarchy is integrable in a liouville sense and possesses bi hamiltonian structure moreover the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenfunctions in particular an explicit n fold darboux transformation for the gi equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique some explicit solitonlike solutions of the gi equation are given by applying its darboux transformation

a discrete variational identity on semi direct sums of lie algebras the discrete variational identity under general bilinear forms on semi direct sums of lie algebras is established the constant involved in the variational identity is determined through the corresponding solution to the stationary discrete zero curvature equation an application of the resulting variational identity to a class of semi direct sums of lie algebras in the volterra lattice case furnishes hamiltonian structures for the associated integrable couplings of the volterra lattice hierarchy

variational identities and applications to hamiltonian structures of soliton equations abstract this is an introductory report concerning our recent research on hamiltonian structures we will discuss variational identities associated with continuous and discrete spectral problems and their applications to hamiltonian structures of soliton equations our illustrative examples are the akns hierarchy and the volterra lattice hierarchy associated with semisimple lie algebras and two hierarchies of their integrable couplings associated with non semisimple lie algebras the resulting hamiltonian structures generate infinitely many commuting symmetries and conservation laws for the four soliton hierarchies the presented variational identities can be applied to hamiltonian structures of other soliton hierarchies

hamiltonian structure of the integrable couplings for the multicomponent dirac hierarchy a scheme for deducing hamiltonian structures of the integrable couplings for the multicomponent hierarchies of evolution equations is presented which is devoting to obtaining the hamiltonian structures of the integrable couplings of the multicomponent dirac hierarchy

a new integrable hierarchy and constrained flows its expanding integrable system abstract a new subalgebra of loop algebra a 2 is first constructed it follows that an isospectral problem is established using tu pattern gives rise to a new integrable hierarchy which possesses bi hamiltonian structure furthermore by making use of bi symmetry constraints the generalized hamiltonian regular representations for the hierarchy are obtained finally we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five dimensional loop algebra g

a bargmann system and the involutive representation of solutions of the levi hierarchy the author considers a linear spectral problem associated with the levi hierarchy of equations a bargmann system under the so called bargmann constraint between the eigenfunctions and potentials is proposed and is proved to be a completely integrable hamiltonian system in the liouville sense moreover by the involutive solution of the compatible systems under the bargmann constraint he presents the involutive representation of solutions of the levi hierarchy especially he obtains the involutive representation of the solution of the well known burgers equation ut uxx 2uux

a liouville integrable hamiltonian system associated with a generalized kaup newell spectral problem abstract starting from a generalized kaup newell spectral problem involving an arbitrary function we derive a hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as kaup newell equation chen lee liu equation gerdjikov ivanov equation burgers equation modified korteweg de vries equation and sharma tasso olever equation it is also shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure

the generalized kupershmidt deformation for the fifth order coupled kdv equations hierarchy abstract based on the kupershmidt deformation we propose the generalized kupershmidt deformation gkd to construct new systems from integrable bi hamiltonian system as applications the generalized kupershmidt deformation of the fifth order coupled kdv equations hierarchy with self consistent sources and its lax representation are presented

finite dimensional discrete systems and integrable systems through nonlinearization of the discrete eigenvalue problem a method is developed that extends the nonlinearization procedure of eigenvalue problems to the discrete case from which the finite dimensional discrete systems and finite dimensional completely integrable systems associated with the toda hierarchy are obtained a new model for solving discrete soliton equations is proposed which enables one to get the solutions of the toda lattice equations by solving the compatible systems of discrete equations and nonlinear ordinary differential equations

a non isospectral integrable couplings of volterra lattice hierarchy with self consistent sources a kind of non isospectral integrable couplings of discrete soliton equations hierarchy with self consistent sources associated with email protected 4 y f zhang e g fan characteristic numbers of matrix lie algebras commun theor phys china 49 2008 845 is presented as an application example the hierarchy of non isospectral cubic volterra lattice hierarchy with self consistent sources is derived furthermore we construct a non isospectral integrable couplings of cubic volterra lattice hierarchy with self consistent sources by using the loop algebra email protected 4

an integrable couplings of dirac soliton hierarchy with self consistent sources abstract a kind of the integrable couplings of soliton equations hierarchy with self consistent sources associated with sl 4 is presented as an application example we construct a new integrable couplings of the dirac soliton hierarchy with self consistent sources by using of loop algebra sl 4

a nonlinear integrable couplings of c kdv soliton hierarchy and its infinite conservation laws abstract a kind of nonlinear integrable couplings of c kdv soliton hierarchy is constructed then we present the infinitely many conservation laws for the nonlinear integrable couplings of the c kdv soliton hierarchy

frequency responses for sampled data systems their equivalence and relationships abstract there are two ways to introduce the notion of frequency response for sampled data systems one is based on the so called lifting and the other based on an interpretation of steady state response in terms of impulse modulation this paper proves the equivalence of these two notions in particular it establishes a more direct link of the second approach to the h norm and also provides the first approach with a natural interpretation of steady state response as an infinite sum of sinusoidal signals this study also leads to a comprehensive account of impulse modulation from the lifting viewpoint

integrable systems of derivative nonlinear schrodinger type and their multi hamiltonian structure a spectral problem and the associated hierarchy of schrodinger type equations are proposed it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure it is found that several kinds of important equation such as the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the modified korteweg de vries equation and the sharma tasso olever equation are members in the hierarchy as its special reductions moreover kn cll and gi equations are described by using a unified generalized derivative schrodinger equation involving a parameter and their hamiltonian structure and lax pairs are also given by unified and explicit formulae

periodic inputs reconstruction of partially measured linear periodic systems in this paper the problem of input reconstruction for the general case of periodic linear systems driven by periodic inputs x a t x a 0 t w t y c t x is addressed where x t r n and a t a 0 t and c t are t 0 periodic matrices and w is a periodic signal containing an infinite number of harmonics the contribution of this paper is the design of a real time observer of the periodic excitation w t using only partial measurement the employed technique estimates the infinite fourier decomposition of the signal although the overall system is infinite dimensional convergence of the observer is proven using a standard lyapunov approach along with classic mathematical tools such as cauchy series parseval equality and compact embeddings of hilbert spaces this observer design relies on a simple asymptotic formula that is useful for tuning finite dimensional filters the presented result extends recent works where full state measurement was assumed here only partial measurement through the matrix c t is considered

a coupled akns kaup newell soliton hierarchy a coupled akns kaup newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from hamiltonian pairs zero curvature representations and tri hamiltonian structures are established for all coupled akns kaup newell systems in the hierarchy therefore all systems have infinitely many commuting symmetries and conservation laws two reductions of the systems lead to the akns hierarchy and the kaup newell hierarchy and thus those two soliton hierarchies also possess tri hamiltonian structures