- 非线性系统及其绝妙的数学结构(第2卷英文)/国外优秀数学著作原版系列
- - 作者：编者:(墨)诺伯特·欧拉//(意)玛丽亚·克拉拉·努奇|责编:张嘉芮//李兰静
  - 出版社：哈尔滨工业大学
  - ISBN：9787576712841
  - 出版日期：2024/10/01
  - 页数：536
- 售价：43.2

内容大纲
本书包含了17篇由非线性系统不同方面的顶尖专家撰写的特邀论文，包括常微分方程和偏微分方程、差分方程、离散或晶格方程、非交换方程和矩阵方程以及时滞方程。本书内容被分为三个主要部分：A部分为可积性，Lax对与对称性，包含7篇论文，作者主要解决了如何检测可积系统的基本问题，以及非线性系统对称方法的使用问题；B部分为代数与几何方法，包含7篇论文，作者描述了获得非线性系统显式解和（或）描述系统解的结构的不同方法；C部分为应用，包含了三篇论文，作者为了解决特殊的非线性问题应用了不同的方法。
作者介绍
目录
Preface
The Authors
A1. Reciprocal transformations and their role in the integrability and classification of PDEs
  1. Introduction
  2. Fundamentals
  3. Reciprocal transformations as a way to identify and classify PDEs
  4. Reciprocal transformations to derive Lax pairs
  5. A Miura-reciprocal transformation
  6. Conclusions
A2. Contact Lax pairs and associated (3+l)-dimensional integrable dispersionless systems
  1. Introduction
  2. Isospectral versus nonisospectral Lax pairs
  3. Lax representations for dispersionless systems in (I+I)D and (2+1)D
  4. Lax reprcsentations for dispersionless systems in (3+l)D
  5. R-matrix approach for dispersionless systems with nonisospectral
  Lax representations
A3. Lax pairs for edge-constrained Boussinesq systems of partial difference equations
  1. Introduction
  2. Gauge equivalence of Lax pairs for PDEs and PAEs
  3. Derivation of Lax pairs for Boussinesq systems
  4. Gauge and gauge-like equivalences of Lax pairs
  5. Application to generalized Hietarinta systems
  6. Summary of results
  7. Software implementation and conclusions
A4. Lie point symmetries of delay ordinary differential equations
  1. Introduction
  2. Illustrating example
  3. Formulation of the problem for first-order DODEs
  4. Construction of invariant first-order DODSs
  5. First-order linearDODSs
  6. Lie symmetry classification of first-order nonlinear DODSs
  7. Exact solutions of the DODSs
  8. Higher order DODSs
  9. Traffic flow micro-model equation
  10. Conclusions
A5. The symmetry approach to integrability: recent advances
  1. Introduction
  2. The symmetry approach to integrability
  3. Integrable non-abelian equations
  4. Non-evolutionary systems
A6. Evolution of the concept of h-symmetry and main applications
  1. Introduction
  2. Basic notions on Lie point symmetries and C∞- symmetries of ODEs
  3. Analytical applications of C~-symmetries
  4. Extensions and geometric interpretations of C∞-symmetries
A7. Heir-equations for partial differential equations: a 25-year review
  1. Introduction
  2. Constructing the heir-equations
  3. Symmetry solutions of heir-equations
  4. Zhdanov's conditional Lie-B~cklund symmetries and heir-equations

  5. Nonclassical symmetries as special solutions of heir-equations
  6. Final remarks
B1. Coupled nonlinear SchrSdinger equations: spectra and instabilities of plane waves
  1. Introduction
  2. Spectra
  3. Dispersion relation and instability
  4. Conclusions
    A. Case r = 0
    B. Polynomials: a tool box
B2. Rational solutions of Painlev systems
  1. Introduction
  2. Dressing chains and Painlevd systems
  3. Hermite T-functions
  4. Hermite-type rational solutions
  5. Cyclic Maya diagrams
  6. Examples of Hermite-type rational solutions
B3. Cluster algebras and discrete integrability
  1. Introduction
  2. Cluster algebras: definition and examples
  3. Cluster algebras with periodicity
  4. Algebraic entropy and tropical dynamics
  5. Poisson and symplectic structures
  6. Discrete Painlev6 equations from coefficient mutation
  7. Conclusions
B4. A review of elliptic difference Painlev6 equations
  1. Introduction
  2. E-lattice
  3. The initial-value space of the RCG equation
  4. Cremona isometrics
  5. Birational actions of the Cremona isometrics for the Jacobi setting
  6. Special solutions of the RCG equation
    A. A-lattice
    B. General elliptic difference equations
B5. Linkage mechanisms governed by integrable deformations of discrete space curves
  1. Introduction
  2. A mathematical model of linkage
  3. Hinged network and discrete space curve
  4. Deformation of discrete curves
  5. Extreme Kaleidocycles
B6. The Cauchy problem of the Kadomtsev=Petviashvili hierarchy and infinite-dimensional groups
  1. Introduction
  2. Diffeologies, Fr51icher spaces and the Ambrose-Singer theorem
  3. Infinite-dimensional Lie groups and pseudodifferential operators
  4. The Cauchy problem for the KP hierarchy
  5. A non-formal KP hierarchy
BT. Wronskian solutions of integrable systems
  1. Introduction
  2. Preliminary
  3. The KdV equation
  4. The mKdV equation

  5. The AKNS and reductions
  6. Discrete case: the lpKdV equation
  7. Conclusions
C1. Global gradient catastrophe in a shallow water model: evolution unfolding by stretched coordinates
  1. Introduction
  2. Exact solutions
  3. Evolution beyond the gradient catastrophe
  4. Discussion and conclusions
C2. Vibrations of an elastic bar isospectral deformations and modified Camassa-Holm equations
  1. Introduction
  2. The Lax formalism: the boundary value problem
  3. Liouville integrability
  4. Forward map: spectrum and spectral data
  5. Inverse problem
  6. Multipeakons for N = 2K
  7. Multipeakons for N = 2K + 1
  8. Reductions of multipeakons
    A. Lax pair for the 2-mCH peakon ODEs
    B. Proof of Theorem 13
    C. Proof of Theorem 17
C3. Exactly solvable (discrete) quantum mechanics and new orthogonal polynomials
  1. Introduction
  2. New orthogonal polynomials in ordinary QM
  3. New orthogonal polynomials in discrete QM with real shifts
  4. Summary and comments
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