On the exact solutions of the Bianchi IX cosmological model in the proper time

It has recently been argued that there might exist a four-parameter analytic solution to the Bianchi IX cosmological model, which would extend the three-parameter solution of Belinskii et al. to one more arbitrary constant. We perform the perturbative Painlev\'e test in the proper time variable, and confirm the possible existence of such an extension.Comment: 8 pages, no figure, standard Latex, to appear in Regular and chaotic dynamics (1998

Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to overcome the difficulties arising in two such methods: (i) the criterium that the sum of residues of an elliptic solution should be zero, (ii) the construction of a first order differential equation admitting the given equation as a differential consequence (subequation method).Comment: 12 pages, no figure, to appear, Theoretical and Mathematical Physic

Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation

I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed description of the spatiotemporally disordered regimes encountered. The nature of the transition lines separating these phases is discussed, and preliminary results are presented which aim at evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic limit.Comment: 14 pages, LaTeX, 9 figures available by anonymous ftp to amoco.saclay.cea.fr in directory pub/chate, or by requesting them to [email protected]

Modelling, kinematic parameter identification and sensitivity analysis of a Laser Tracker having the beam source in the rotating head

This paper presents a new kinematic model, a parameter identification procedure and a sensitivity analysis of a laser tracker having the beam source in the rotating head. This model obtains the kinematic parameters by the coordinate transformation between successive reference systems following the Denavit–Hartenberg method. One of the disadvantages of laser tracker systems is that the end-user cannot know when the laser tracker is working in a suitable way or when it needs an error correction. The ASME B89.4.19 Standard provides some ranging tests to evaluate the laser tracker performance but these tests take a lot of time and require specialized equipment. Another problem is that the end-user cannot apply the manufacturer’s model because he cannot measure physical errors. In this paper, first the laser tracker kinematic model has been developed and validated with a generator of synthetic measurements using different meshes with synthetic reflector coordinates and known error parameters. Second, the laser tracker has been calibrated with experimental data using the measurements obtained by a coordinate measuring machine as nominal values for different strategies, increasing considerably the laser tracker accuracy. Finally, a sensitivity analysis of the length measurement system tests is presented to recommend the more suitable positions to perform the calibration procedure

Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians

The quartic H\'enon-Heiles Hamiltonian $H = (P_1^2+P_2^2)/2+(\Omega_1 Q_1^2+\Omega_2 Q_2^2)/2 +C Q_1^4+ B Q_1^2 Q_2^2 + A Q_2^4 +(1/2)(\alpha/Q_1^2+\beta/Q_2^2) - \gamma Q_1$ passes the Painlev\'e test for only four sets of values of the constants. Only one of these, identical to the traveling wave reduction of the Manakov system, has been explicitly integrated (Wojciechowski, 1985), while the three others are not yet integrated in the generic case $(\alpha,\beta,\gamma)\not=(0,0,0)$. We integrate them by building a birational transformation to two fourth order first degree equations in the classification (Cosgrove, 2000) of such polynomial equations which possess the Painlev\'e property. This transformation involves the stationary reduction of various partial differential equations (PDEs). The result is the same as for the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases, a general solution which is meromorphic and hyperelliptic with genus two. As a consequence, no additional autonomous term can be added to either the cubic or the quartic Hamiltonians without destroying the Painlev\'e integrability (completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200

Solitary waves of nonlinear nonintegrable equations

Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonperturbative, are classified in two classes. In the first class, which includes the well known so-called truncation methods, one \textit{a priori} assumes a given class of expressions (polynomials, etc) for the unknown solution; the involved work can easily be done by hand but all solutions outside the given class are surely missed. In the second class, instead of searching an expression for the solution, one builds an intermediate, equivalent information, namely the \textit{first order} autonomous ODE satisfied by the solitary wave; in principle, no solution can be missed, but the involved work requires computer algebra. We present the application to the cubic and quintic complex one-dimensional Ginzburg-Landau equations, and to the Kuramoto-Sivashinsky equation.Comment: 28 pages, chapter in book "Dissipative solitons", ed. Akhmediev, to appea

Construction of Special Solutions for Nonintegrable Systems

The Painleve test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonometric ones. The standard methods for constructing the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and a search for solutions of the obtained system. It has been demonstrated by the example of the generalized Henon-Heiles system that the use of the Laurent series solutions of the initial differential equation assists to solve the obtained algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial differential equation in the form of the Laurent or Puiseux series we use the Painleve test. This test can also assist to solve the inverse problem: to find the form of a polynomial potential, which corresponds to the required type of solutions. We consider the five-dimensional gravitational model with a scalar field to demonstrate this.Comment: LaTeX, 14 pages, the paper has been published in the Journal of Nonlinear Mathematical Physics (http://www.sm.luth.se/math/JNMP/

Walking Through the Method Zoo: Does Higher Education Really Meet Software Industry Demands?

Software engineering educators are continually challenged by rapidly evolving concepts, technologies, and industry demands. Due to the omnipresence of software in a digitalized society, higher education institutions (HEIs) have to educate the students such that they learn how to learn, and that they are equipped with a profound basic knowledge and with latest knowledge about modern software and system development. Since industry demands change constantly, HEIs are challenged in meeting such current and future demands in a timely manner. This paper analyzes the current state of practice in software engineering education. Specifically, we want to compare contemporary education with industrial practice to understand if frameworks, methods and practices for software and system development taught at HEIs reflect industrial practice. For this, we conducted an online survey and collected information about 67 software engineering courses. Our findings show that development approaches taught at HEIs quite closely reflect industrial practice. We also found that the choice of what process to teach is sometimes driven by the wish to make a course successful. Especially when this happens for project courses, it could be beneficial to put more emphasis on building learning sequences with other courses

Generalized Lenard Chains, Separation of Variables and Superintegrability

We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional \omega N manifold guarantees the separation of variables. As an application, we construct such chains for the H\'enon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.Comment: 14 pages Revte