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Discretegroup 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.

Eisenhower C LevelQA 372 .Z3513 1994 c. 1Available
 Also known as
 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 RFPairs. 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 EmdenFowler 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 EmdenFowler 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: QuasiHomogeneous 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 EmdenFowler Equation. 3.8. Constructing Abel Equations Using a Single 12Parameter Equation of the First Order. 3.9. Some Second and ThirdOrder 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 NonNewtonian Liquids. 4.5. Classical ThermalExplosion Problem. 4.6. Hydrodynamic Thermal Explosion in NonNewtonian 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 EmdenFowler Equation [actual symbol not reproducible]
 Supplement 2. Nonlinear Differential Equations Containing Arbitrary Functions.
 Other information

 Includes bibliographical references (p. 291294) and index.
 ISBN

 0849399165
 Identifying numbers

 LCCN: 93008743
 OCLC: 28255653