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  1. Method of Invariant Grids

    The method of invariant grids is developed for a grid-based computation of invariant manifolds.
    Alexander N. Gorban, Ilya V. Karlin in Invariant Manifolds for Physical and Chemical Kinetics
    Chapter

  2. Mathematical Notation and Some Terminology

    – The operator L from space W to space E: L : W → E
    Alexander N. Gorban, Ilya V. Karlin in Invariant Manifolds for Physical and Chemical Kinetics
    Chapter

  3. References

    Alexander N. Gorban, Ilya V. Karlin in Invariant Manifolds for Physical and Chemical Kinetics
    Chapter

  4. Invariance Equation in Differential Form

    Definition of invariance in terms of motions and trajectories assumes, at least, existence and uniqueness theorems for solutions of the original...
    Alexander N. Gorban, Ilya V. Karlin in Invariant Manifolds for Physical and Chemical Kinetics
    Chapter

  5. Entropy, Quasiequilibrium, and Projectors Field

    Projection operators Py contribute both to the invariance equation (3.2), and to the film extension of the dynamics (4.5). Limiting results, exact...
    Alexander N. Gorban, Ilya V. Karlin in Invariant Manifolds for Physical and Chemical Kinetics
    Chapter

  6. 1 Introduction

    The class of block-oriented nonlinear models includes complex models which are composed of linear dynamic systems and nonlinear static elements....
    Andrzej Janczak in Identification of Nonlinear Systems Using Neural Networks and Polynomial Models
    Chapter

  7. Results for Sr2RuO4

    In this chapter, we focus on our results for the elementary excitations and Cooper pairing in strontium ruthenate (...
    Dirk Manske in Theory of Unconventional Superconductors
    Chapter

  8. 10. Main sychronization

    It was made clear in Chapter 9 that the second order type-II loop operates either in saturated or in unsaturated mode. In this chapter, only the main...
    Nikolaos I. Margaris in Theory of the Non-linear Analog Phase Locked Loop
    Chapter

  9. 4. Main synchronization

    In this chapter the main synchronization of the first order PLL is discussed. At first, we perform the local stability analysis of the main...
    Nikolaos I. Margaris in Theory of the Non-linear Analog Phase Locked Loop
    Chapter

  10. 8. Main synchronization

    In the present chapter the main synchronization of the second order type-I loop is treated. At first, the local stability analysis is presented and...
    Nikolaos I. Margaris in Theory of the Non-linear Analog Phase Locked Loop
    Chapter

  11. Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method

    We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e....
    Micheline Musette in Direct and Inverse Methods in Nonlinear Evolution Equations
    Chapter

  12. 11. Third harmonic synchronization

    In this chapter, a brief analysis of the synchronization at the third harmonic of the center VCO frequency is given. The relatively large width of...
    Nikolaos I. Margaris in Theory of the Non-linear Analog Phase Locked Loop
    Chapter

  13. 6. Introduction to second order type – I PLL

    From the analysis of the first order loop, presented in Part I, it becomes evident that the presence of the ripple in the output of the phase...
    Nikolaos I. Margaris in Theory of the Non-linear Analog Phase Locked Loop
    Chapter

  14. 12. Introduction to third order type – II PLL

    According to the analysis presented in Part IV, the presence of ripple makes the performance of the second order type-II loop problematic. Therefore,...
    Nikolaos I. Margaris in Theory of the Non-linear Analog Phase Locked Loop
    Chapter

  15. Theory of Cooper Pairing Due to Exchange of Spin Fluctuations

    It is of general interest whether singlet high- \(T_{\rm c}\)...
    Dirk Manske in Theory of Unconventional Superconductors
    Chapter

  16. 14. Third harmonic sychronization

    In this chapter we will present a brief analysis of the synchronization at the third harmonic of the center VCO frequency for the third order type-II...
    Nikolaos I. Margaris in Theory of the Non-linear Analog Phase Locked Loop
    Chapter

  17. 9. Introduction to second order type – II PLL

    In the second order type-II loop the filter is active and specifically a PI controller. This loop is considered superior to the second order type-I...
    Nikolaos I. Margaris in Theory of the Non-linear Analog Phase Locked Loop
    Chapter

  18. Nonlinear Waves, Solitons, and IST

    These lectures are written for a wide audience with diverse backgrounds. The subject is approached from a general perspective and overly detailed...
    M.J. Ablowitz in Integrability of Nonlinear Systems
    Chapter

  19. Integrability – and How to Detect It

    We present a physicist’s approach to integrability and its detection. Starting from specific examples we present a working definition of what is...
    B. Grammaticos, A. Ramani in Integrability of Nonlinear Systems
    Chapter

  20. Bilinear Formalism in Soliton Theory

    A brief survey of the bilinear formalism discovered by Hirota is given. First, the procedure to obtain soliton solutions of nonlinear evolution...
    J. Satsuma in Integrability of Nonlinear Systems
    Chapter
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