Book, Print in English

Discrete-group methods for integrating equations of nonlinear mechanics: theory, solutions, and applications

V.F. Zaitsev and Andrei D. Polyanin ; translator Mark A. Piterman ; English edition editors T.W. Wilcox and John C. Friedly.
  • Boca Raton, FL : CRC Press, ©1994.
  • x, 302 pages ; 26 cm.
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Subjects
Contents
  • 1. Discrete Group Analysis. 1.1. Introduction: Basic Notation and Definitions. 1.2. Discrete Transformation Groups and Their Graphs. 1.3. Transformation Classes and RF-Pairs. 1.4. Methods of Searching for Point Transformations. 1.5. Methods of Searching for Backlund Transformations. 1.6. Singular Points of Discrete Groups. 1.7. Invariants of Discrete Groups. 1.8. Nonlocal Transformations of Autonomous Equations
  • 2. Symmetries and Nets of Solvable Cases for Specific Classes of Equations. 2.1. Symmetry of the Class of Equations [actual symbol not reproducible]: The Imbedding Method. 2.2. Extensions of Groups Admitted by the Class of Generalized Emden-Fowler Equations: Solvable Class Orbits. 2.3. Transformations and Some Solvable Cases of Classes of Polynomial Equations (2.1.2) and (2.1.3). 2.4. Symmetries and a Network of Solvable Cases for the Equation [actual symbol not reproducible]. 2.5. Symmetries and a Network of Solvable Cases for the Equation [actual symbol not reproducible].
  • 2.6. Integration of the Discrete Invariant Equations
  • 3. Abel's Equations. 3.1. Abel's Equations of the Second Kind: Canonical Transformations. 3.2. Mappings of Discrete Groups of Transformations: Relation Between the Generalized Emden-Fowler Equation and Abel Equations. 3.3. Application of Group Methods for the Search for Solvable Abel Equations. 3.4. One Approach to the Search for Solvable Abel Equations: Quasi-Homogeneous Equations. 3.5. Simplest Examples of the Construction of Solvable Abel Equations. 3.6. Construction of Solvable Abel Equations Using the Riccati Equation. 3.7. Some Nonlinear Transformations of Abel Equations Associated with the Emden-Fowler Equation. 3.8. Constructing Abel Equations Using a Single 12-Parameter Equation of the First Order. 3.9. Some Second- and Third-Order Equations Reducible to Abel Equations
  • 4. Equations and Problems of Nonlinear Mechanics. 4.1. Heat Conduction with Variable Transfer Coefficient. 4.2. Nonlinear Problems of Diffusion Boundary Layer.
  • 4.3. Boundary Layer Equation for Exponential Liquids. 4.4. Dynamics of a Spherical Bubble in Non-Newtonian Liquids. 4.5. Classical Thermal-Explosion Problem. 4.6. Hydrodynamic Thermal Explosion in Non-Newtonian Liquids. 4.7. Some Nonlinear Convective Thermal Effects in the Theory of Percolation. 4.8. Nonisothermal Flows of Liquids at a Variable Tube Wall Temperature. 4.9. Multiplicity of Stationary Regimes in the Theory of Chemical Reactors. 4.10. Equations of Nonlinear Oscillations. 4.11. Use of Electric Current for Heating a Medium: Examples of Discrete Transformations of Partial Differential Equations
  • Supplements: Certain Types of Differential Equations and Their Solutions
  • Supplement 1. The Generalized Emden-Fowler Equation [actual symbol not reproducible]
  • Supplement 2. Nonlinear Differential Equations Containing Arbitrary Functions.
Other information
  • Includes bibliographical references (p. 291-294) and index.
ISBN
  • 0849399165
Identifying numbers
  • LCCN: 93008743
  • OCLC: 28255653