group classification of schrodinger equations with position dependent mass maximal kinematical invariance groups of the schrodinger equations with position dependent mass pdm and arbitrary potential are classified it is demonstrated that there exist seven classes of such equations possessing non equivalent continuous symmetry group three of these classes include arbitrary functions while the remaining ones are defined up to arbitrary parameters in particular for the case of a constant mass the class missing in the boyer classification boyer 1974 helv phys acta 47 450 is indicated a constructive test of non equivalence of a pdm system to a constant mass system is proposed

isomorphisms between quantum group covariant q oscillator systems defined for q and q 1 it is shown that there exists an isomorphism between q oscillator systems covariant under suq n and suq 1 n by the isomorphism the defining relations of a suq 1 n covariant q oscillator system are transmuted into those of suq n it is also shown that a similar isomorphism exists for the system of q oscillators covariant under the quantum supergroup suq n m furthermore the cases of q deformed lie super algebras constructed from covariant q oscillator systems are considered the isomorphisms between q deformed lie super algebras cannot be obtained by the direct generalization of the isomorphism for covariant q oscillator systems

feedback linearization and stabilization of second order non holonomic chained systems this paper presents a theoretical framework for non regular feedback linearization and stabilization of second order non holonomic chained systems by giving a new criterion for the problem of non smooth non regular feedback linearization it is proved that second order chained systems are non regular static state feedback linearizable a discontinuous control law is obtained based on linear system theory and the inversion technique the design mechanism is generalized to higher order non holonomic chained systems simulation studies are carried out to show the effectiveness of the approach

comments on adaptive global stabilization of nonholonomic systems with strong nonlinear drifts systems control letters 46 2002 195 205 in the paper to be commented there is a technical problem inherent in the input based switching and it is highlighted here to avoid possible failure when the scheme is used in practice

symmetry classes of variable coefficient nonlinear schrodinger equations a variable coefficient nonlinear schrodinger vcnls equation involving three arbitrary complex functions of space time in 1 1 dimensions is analysed from the point of view of its symmetries all equations of the type studied having non trivial lie point symmetry groups g are identified the symmetry group is shown to be at most five dimensional and only when the equation is equivalent to the nls equation itself or to a rather special complex ginzburg landau equation lie point transformations are used to obtain solutions of specific vcnls equations that should be of interest in nonlinear optics or other branches of physics

conditional symmetry of a porous medium equation abstract we obtain an exhaustive description of conditional symmetries admitted by a nonlinear porous medium equation in one spatial dimension it is proved that solving the determining equations for the conditional symmetries either yields classical lie symmetries or is equivalent to solving the porous medium equation itself the second possibility is shown to be typical for an arbitrary evolution type partial differential equation in one spatial variable we show that this very property is responsible for the well known phenomenon when using non classical symmetries yield exact solutions which prove to be invariant ones

a group classification of the general second order coupled diffusion system we classify second order systems of coupled heat diffusion equations the underlying system contains several unknown functions the forms of which are specified via the method of group classification in particular the canonical forms of the low dimensional lie algebras and the lie algebras of higher dimension provide a means to specify the functional forms of these arbitrary functions

symmetry reductions and exact solutions of a class of nonlinear heat equations abstract classical and nonclassical symmetries of the nonlinear heat equation ut uxx f u are considered the method of differential grobner bases is used both to find the conditions on f u under which symmetries other than the trivial spatial and temporal translational symmetries exist and to solve the determining equations for the infinitesimals a catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of the nonlinear heat equation for cubic f u in terms of the roots of f u 0

group classification of systems of non linear reaction diffusion equations with general diffusion matrix i generalized ginzburg landau equations abstract a group classification of the generalized complex ginzburg landau equations is presented an approach to group classification of systems of reaction diffusion equations with general diffusion matrix is formulated

classification of coupled systems with two component nonlinear diffusion equations by the invariant subspace method the invariant subspace method is developed to perform classification of systems with two component nonlinear diffusion equations which was carried out with respect to the invariant subspaces defined by linear ordinary differential equations as a result the corresponding exact solutions generated by invariant subspaces to the resulting systems are obtained in most cases two components of these exact solutions belong to different scalar subspaces behaviour to several exact solutions of the systems is described

on the simplification of the form of lie transformation groups admitted by systems of evolution differential equations abstract for a system of two partial differential equations in two independent variables the lie point symmetry generator has the form t x u v t t x u v x t x u v u t x u v v we consider a system of evolution equations of general class and we provide restrictions on the functional forms of the coefficient functions of the lie generator these restrictions reduce the amount of calculations in determining the lie symmetries of the system under study we show that t except in one special case and we present further restrictions on the remaining coefficient functions

a switching algorithm for global exponential stabilization of uncertain chained systems this note deals with chained form systems with strongly nonlinear unmodeled dynamics and external disturbances the objective is to design a robust nonlinear state feedback law such that the closed loop system is globally kexponentially stable we propose a novel switching control strategy involving the use of input state scaling and integrator backstepping the new features of our controllers include the ability to achieve lyapunov stability exponential convergence and robustness to a set of uncertain drift terms

adaptive global stabilization of nonholonomic systems with strong nonlinear drifts a new input to state scaling scheme is first introduced to transform a class of nonholonomic systems in a chained form with strong nonlinear drifts and unknown constant parameters into a strict feedback form the backstepping technique is then applied to design a global adaptive stabilization controller a switching strategy based on the control input magnitude rather than the time is derived to get around the phenomenon of uncontrollability simulation examples validate the effectiveness of the proposed controller

output feedback adaptive stabilization control design for non holonomic systems with strong non linear drifts this paper investigates the problem of output feedback adaptive stabilization control design for non holonomic chained systems with strong non linear drifts including modelled non linear dynamics unmodelled dynamics and those modelled but with unknown parameters an observer and an estimator are introduced for state and parameter estimates respectively by using the integrator backstepping approach and based on the observer and parameter estimator a constructive design procedure for output feedback adaptive stabilization control is given it is shown that under some conditions the control design ensures the closed loop system is globally asymptotically stable when there is no non linear drift in the first subsystem and semiglobally asymptotically stable otherwise an example is given to show the effectiveness of the theory

group classification of systems of non linear reaction diffusion equations with general diffusion matrix ii generalized turing systems abstract group classification of systems of two coupled non linear reaction diffusion equation with a diagonal diffusion matrix is carried out symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described

preliminary group classification of the nonlinear differential difference equations abstract preliminary group classification of the nonlinear differential difference equations of the form u n f n t u n 1 u n u n 1 is considered by using the classical infinitesimal lie method and the theory of classification of abstract low dimensional lie algebras restrict to lie point symmetries and assume that the lie algebra of the symmetry group is realized by a particular vector field it is proved that there is only one equation admitting three dimensional simple lie algebras what is more all the inequivalent equations admitting semi simple lie algebras are nothing but the one also there exist inequivalent equations admitting low dimensional solvable lie algebras and semi direct sums of semi simple and solvable lie algebras

discontinuous control of nonholonomic systems the problem of asymptotic convergence for a class of nonholonomic control systems via discontinuous control is addressed and solved from a new point of view it is shown that control laws which ensures asymptotic exponential convergence of the closed loop system can be easily designed if the system is described in proper coordinates in such coordinates the system is discontinuous hence the problem of local asymptotic stabilization for a class of discontinuous nonholonomic control systems is dealt with and a general procedure to transform a continuous system into a discontinuous one is presented moreover a general strategy to design discontinuous control laws yielding asymptotic convergence for a class of nonholonomic control systems is proposed the enclosed simulation results show the effectiveness of the method

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

systems of reaction convection diffusion equations invariant under galilean algebras abstract systems which are invariant under galilean algebras with and without mass operator and their main extensions by operators of scale and projective transformations are selected from a class of systems of reaction convection diffusion equations for two dimensional vector field with one space variable

systems of reaction diffusion equations and their symmetry properties a constructive algorithm is proposed for the investigation of symmetries of partial differential equations the algorithm is used to present classical lie symmetries of systems of two nonlinear reaction diffusion equations