liouville integrability of the finite dimensional hamiltonian systems derived from principal chiral field for finite dimensional hamiltonian systems derived from 1 1 dimensional integrable systems if they have lax representations then the lax operator creates a set of conserved integrals when these conserved integrals are in involution it is believed quite popularly that there will be enough functionally independent ones among them to guarantee the liouville integrability of the hamiltonian systems at least for those derived from physical problems in this article we give a counterexample based on the u 2 principal chiral field it is proved that the finite dimensional hamiltonian systems derived from the u 2 principal chiral field are liouville integrable moreover their lax operator gives a set of involutive conserved integrals but they are not enough to guarantee the integrability of the hamiltonian systems

a new orthogonal series approach to state space analysis of bilinear systems in this note a new orthogonal series approach to state space analysis of bilinear time invariant systems is presented the present approach involves only multiplications of matrices of small dimensions known techniques involve the solution of an algebraic system with a very large number of equations

existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media we prove the existence of multidimensional traveling wave solutions to the scalar equation for the transport of solutes contaminants with nonlinear adsorption and spatially periodic convection diffusion adsorption coefficients under the assumption that the nonlinear adsorption function satisfies the lax and oleinik entropy conditions in the nondegenerate case we also prove the uniqueness of the traveling waves these traveling waves are analogues of viscous shock profiles they propagate with effective speeds that depend on the periodic porous media only up to their mean states and are given by an averaged rankine hugoniot relation this is a direct consequence of the fact that the transport equation is in conservation form we use the sliding domain method the continuation method spectral theory maximum principles and a priori estimates in the degenerate case the traveling waves are weak solutions of a degenerate parabolic equation and are only holder continuous we obtain them by taking suitable limits on the non degenerate traveling waves the uniqueness of the degenerate traveling waves is open

analysis of bilinear systems via single term walsh series this paper presents a new method of analysis of bilinear systems via the single term walsh series stws the stws method has definite advantages over the walsh function wf method and block pulse function bpf method both the discrete values and block pulse values of the results are obtained for any length of time and selecting any positive integer as the number of intervals the recursive relations are simple and save both computer time and storage illustrative examples are presented

integrable decomposition of a hierarchy of soliton equations and integrable coupling system by semidirect sums of lie algebras abstract staring from a new spectral problem a hierarchy of the soliton equations is derived it is shown that the associated hierarchies are infinite dimensional integrable hamiltonian systems by the procedure of nonlinearization of the lax pairs the integrable decomposition of the whole soliton hierarchy is given further we construct two integrable coupling systems for the hierarchy by the conception of semidirect sums of lie algebras

geometric optics approach to reaction diffusion equations the speed of propagation of traveling waves of reaction diffusion equations is calculated by an asymptotic method similar to geometrical optics this also works for reaction diffusion waves in random media

reaction diffusion fronts in periodically layered media we compute the effective wavefront speeds of reaction diffusion equations in periodically layered media with coefficients that have small amplitude oscillations around a uniform mean state we compare them with the corresponding wavefront speeds in the uniform state we analyze a one dimensional model where wave propagation is along the layering direction of the medium and a two dimensional shear flow model where wave propagation is othogonal to the layering direction we find that the effective wave speed is smaller in the one dimensional model and is larger in the two dimensional model for both bistable cubic and quadratic nonlinearities of the kolmogorov petrovskii piskunov form we derive approximate expressions for the wave speeds in the bistable case

analysis of bilinear systems using walsh functions by using walsh functions to analyze bilinear systems it is shown that the nonlinear differential system equation can be converted to a linear algebraic generalized lyapunov equation that can be solved for the coefficients of the state x t in terms of the walsh basis functions this lyapunov equation provides an approximate closed form solution for a bilinear system some guidelines are given for selecting the number of terms in the walsh approximating series

analysis and parameter estimation of bilinear systems via block pulse functions problems of analysis and parameter estimation of bilinear systems via block pulse functions are discussed and recursive algorithms convenient for computers are presented compared with walsh function approaches the results are much simpler in form in this method any positive integer can be chosen as the number of sub intervals consequently much computing time and storage can be saved and the recursive algorithms developed also make it possible to identify on line the parameters of bilinear systems

bistable transition fronts in rn abstract this paper is chiefly concerned with qualitative properties of some reaction diffusion fronts the recently defined notions of transition fronts generalize the standard notions of traveling fronts in this paper we show the existence and the uniqueness of the global mean speed of bistable transition fronts in r n this speed is proved to be independent of the shape of the level sets of the fronts the planar fronts are also characterized in the more general class of almost planar fronts with any number of transition layers these qualitative properties show the robustness of the notions of transition fronts but we also prove the existence of new types of transition fronts in r n that are not standard traveling fronts thus showing that the notions of transition fronts are broad enough to include other relevant propagating solutions

analysis and parameter identification of bilinear systems via shifted legendre polynomials the problems of analysis and parameter identification of lime delay systems have been recently studied using rectangular functions such as walsh and block pulse functions in this paper the continuous shifted legendre polynomials are first used to solve the above mentioned problems the approach followed is that of converting the delay differential equation to an algebraic form through using the operational matrices of integration and delay the key point is the derivation of a delay operational matrix d which relates the coefficient vector x of the shifted legendre series of a given function x t with the coefficient vector x of its delay form x t in the form x dx where the elements of a are obtained from the initial function of x t two computational examples are given to illustrate the utility of the method the availability of recursive algorithms for constructing the delay operational matrix d makes the method particularly attractive to practise

existence of planar flame fronts in convective diffusive periodic media we prove the existence of planar travelling wave solutions in a reaction diffusion convection equation with combustion nonlinearity and self adjoint linear part in rn n 1 the linear part involves diffusion convection terms and periodic coefficients these travelling waves have wrinkled flame fronts propagating with constant effective speeds in periodic inhomogeneous media we use the method of continuation spectral theory and the maximum principle uniqueness and monotonicity properties of solutions follow from a previous paper these properties are essential to overcoming the lack of compactness and the degeneracy in the problem

harmonic maps into lie groups classical solutions of the chiral model on considere deux aspects de la structure algebrique de 7b m l espace des applications harmoniques d un domaine a 2 dimensions simplement connexe dans un groupe de lie reel g r la forme reelle d un groupe complexe g on construit une representation du groupe boucle 7b a s 1 g r sur 7b m correspondant a l algebre de lie de kacmoody des deformations infinitesimales on decrit l action sur 7b m et l action d un sous groupe sur l espace des applications harmoniques dans des gaussmanniens dans une seconde partie on se restreint a une theorie qui s applique seulement quand est un domaine riemannien a 2 dimensions simplement connexe et le groupe est g r u n

analysis and parameter estimation of bilinear systems via generalized orthogonal polynomials abstract an effective method of using generalized orthogonal polynomials gop for analysing and identifying the parameters of a process whose behaviour can be modelled by a bilinear equation is presented the integration operational matrix and the operational matrix for the product of ti with the gop vector are derived these two kinds of operational matrices of the gop are related to any type of individual orthogonal polynomial by expanding the state and control functions into a series of gop the bilinear equation can be converted into a set of linear algebraic equations the expansion coefficients of state variables are solved from these linear algebraic equations the unknown parameters are evaluated by using the least squares method in conjunction with the individual orthogonal polynomial expansion two examples are given to illustrate the validity of the method very satisfactory results are obtained

existence and nonexistence of traveling waves and reaction diffusion front propagation in periodic media we review the existence results of traveling wave solutions to the reaction diffusion equations with periodic diffusion convection coefficients and combustion bistable nonlinearities we prove that whenever traveling waves exist the solutions of the initial value problem with either frontlike or pulselike data propagate with the constant effective speeds of traveling waves in all suitable directions in the case of bistable nonlinearity and one space dimension we give an example of nonexistence of traveling waves which causes quenching localization of wavefront propagation quenching localization only occurs when the variations of the media from their constant mean values are large enough our related numerical results also provide evidence for this phenomenon in the parameter regimes not covered by the analytical example finally we comment on the role of the effective wave speeds in determining the effective wavefront equation hamilton jacobi equation of the reactiondiffusion equations under the small diffusion fast reaction limit with a formal geometric optics expansion

algebro geometric solution of the 2 1 dimensional burgers equation with a discrete variable the quasiperiodic solution of the 2 1 dimensional burgers equation with a discrete variable is obtained through three steps a decomposition into a symplectic map plus two finite dimensional hamiltonian systems b straightening out of both the discrete and the continuous flows in the jacobian variety c inversion into the original variables inner relation with the modified kadomtsev petviashvili equation is presented the explicit theta function solutions for these two 2 1 integrable models are given

ricci deformation of the metric on complete noncompact riemannian manifolds soit m une variete de riemann complete non compacte a n dimensions n 3 pour c1 c2 0 et 0 il existe une constante e e n c1 c2 0 telle que si la courbure de m satisfait a vol b x y c 1 n x m 0 et b rm 2 er 2 0 r c 2 x 0 x 2 x m alors l equation d evolution g ij t t 2r ij t g ij 0 g ij a une solution pour tout temps 0 t et la metrique g ij t converge vers une metrique lisse g ij quand t telle que r ijkl 0 sur m

new factorization of the kaup newell hierarchy abstract the new factorizations of each equation in the kaup newell kn hierarchy into two commuting x and t n finite dimensional integrable hamiltonian systems fdihs via the higher order potential eigenfunction constraints are presented the integrability commutativity and lax representation for these fdihss are deduced from the adjoint representations of the auxiliary linear problems for the kn hierarchy this approach provides a natural way to study soliton hierarchies with source the zero curvature representation and darboux transformation for the kn hierarchy with source related to eigenfunctions are found

twisted and conical kahler ricci solitons on fano manifolds in this paper we first study the relationship between the existence of twisted kahler ricci solitons and the properness of modified twisted k energy approximating by a sequence of smooth twisted kahler ricci solitons we obtain an existence result of conical kahler ricci solitons

the finite band solution of the jaulent miodek equation a method to construct the finite band solution to the soliton equation is presented we take the jaulent miodek equation as an example with the use of the nonlinearization of lax pair the jaulent miodek equation is decomposed into two finite dimensional integrable systems whose properties are studied from the view of an r matrix then through solving these finite dimensional integrable systems the finite band solution of the jaulent miodek equation is obtained

new li yau hamilton inequalities for the ricci flow via the space time approach we prove li yau hamilton inequalties that extend hamilton s matrix inequality for solutions of the ricci flow with nonnegative curvature operators to obtain our extensions we apply the space time formalism of s c chu and one of the authors to solutions of the ricci flow modified by a cosmological constant then we adjoin to the ricci flow the evolution of a 1 form and a 2 form flowing by a system of heat type equations by a rescaling argument the inequalities we obtain in this manner yield new inequalities which are reminiscent of the linear trace inequality of hamilton and one of the authors

binary symmetry constraints of n wave interaction equations in 1 1 and 2 1 dimensions binary symmetry constraints of the n wave interaction equations in 1 1 and 2 1 dimensions are proposed to reduce the n wave interaction equations into finite dimensional liouville integrable systems a new involutive and functionally independent system of polynomial functions is generated from an arbitrary order square matrix lax operator and used to show the liouville integrability of the constrained flows of the n wave interaction equations the constraints on the potentials resulting from the symmetry constraints give rise to involutive solutions to the n wave interaction equations and thus the integrability by quadratures are shown for the n wave interaction equations by the constrained flows

a 3 sx 3 matrix spectral problem for akns hierarchy and its binary nonlinearization abstract a 3 3 matrix spectral problem for akns soliton hierarchy is introduced and the corresponding bargmann symmetry constraint involving lax pairs and adjoint lax pairs is discussed an explicit new poisson algebra is proposed and thus the liouville integrability is established for the nonlinearized spatial system ind a hierarchy of nonlinearized temporal systems under the control of the nonlinearized spatial system the obtained nonlinearized lax systems in which the nonlinearized spatial system is intimately related to stationary akns flows lead to a sort of new involutive solutions to each akns soliton equation therefore the binary nonlinearization theory is successfully extended to a case of 3 3 matrix spectral problem for akns hierarchy

structure analysis via orthogonal functions the use of orthogonal functions to analyse the structure of a system is investigated applying the definitions of observability and controllability to a system that is approximated with the help of orthogonal functions it is shown that the concepts of the state space and the space of orthogonal functions are equivalent provided that two weak conditions are met this result ensures that the observability and controllability properties remain invariant under the transformation introduced by the approximation furthermore new criteria to test observability and controllability are given in terms of the coefficient matrix of the orthogonal expansion because this test does not require the knowledge of the system matrices a b and c the results derived may be used for the identification of systems it is demonstrated that all the results obtained remain true even for an approximation with low accuracy these properties allow the application of orthogonal functions for the analysis of systems

complete riemannian manifolds with pointwise pinched curvature an analogous bonnet myers theorem is obtained for a complete and positively curved n dimensional n 3 riemannian manifold m n we prove that if n 4 and the curvature operator of m n is pointwise pinched or if n 3 and the ricci curvature of m 3 is pointwise pinched then m n is compact

integrable maps for the garnier and for the neumann system we construct integrable maps for the garnier and for the neumann system they are related to the toda hierarchy exactly in the same way as the garnier and the neumann systems are related to the kdv hierarchy as restricted flows here we give lax representations for these maps and prove that they are completely integrable

mathematical analysis of a three dimensional eutrophication model abstract in this paper we present and analyze a nutrient phytoplankton zooplankton organic detritus dissolved oxygen mathematical model simulating eutrophication processes into aquatic media as a main result we obtain existence and uniqueness results for the solution of the system under realistic hypotheses of non smooth coefficients in particular a non regular water velocity this lack or regularity prevent us from using the standard semigroup approach forcing us towards the utilization of more refined techniques