TY  - BOOK
AU  - Hydon,Peter E.
ED  - Cambridge University Press.
TI  - Symmetry methods for differential equations: a beginner's guide 
T2  - Cambridge texts in applied mathematics
SN  - 0521497035
AV  - QC20.7.D5 H93 2000
PY  - 2000///
CY  - Cambridge, New York
PB  - Cambridge University Press
KW  - Differential equations
KW  - Numerical solutions
KW  - Symmetry
KW  - Mathematical physics
N1  - Includes bibliographical references (pages 209-210) and index; Preface	; 	Acknowledgements	; 1	Introduction to Symmetries	1; 	1.1	Symmetries of Planar Objects	1; 	1.2	Symmetries of the Simplest ODE	5; 	1.3	The Symmetry Condition for First-Order ODEs	8; 	1.4	Lie Symmetries Solve First-Order ODEs	11; 2	Lie Symmetries of First-Order ODEs	15; 	2.1	The Action of Lie Symmetries on the Plane	15; 	2.2	Canonical Coordinates	22; 	2.3	How to Solve ODEs with Lie Symmetries	26; 	2.4	The Linearized Symmetry Condition	30; 	2.5	Symmetries and Standard Methods	34; 	2.6	The Infinitesimal Generator	38; 3	How to Find Lie Point Symmetries of ODEs	43; 	3.1	The Symmetry Condition	43; 	3.2	The Determining Equations for Lie Point Symmetries	46; 	3.3	Linear ODEs	52; 	3.4	Justification of the Symmetry Condition	54; 4	How to Use a One-Parameter Lie Group	58; 	4.1	Reduction of Order by Using Canonical Coordinates	58; 	4.2	Variational Symmetries	63; 	4.3	Invariant Solutions	68; 5	Lie Symmetries with Several Parameters	74; 	5.1	Differential Invariants and Reduction of Order	74; 	5.2	The Lie Algebra of Point Symmetry Generators	79; 	5.3	Stepwise Integration of ODEs	89; 6	Solution of ODEs with Multiparameter Lie Groups	93; 	6.1	The Basic Method: Exploiting Solvability	93; 	6.2	New Symmetries Obtained During Reduction	99; 	6.3	Integration of Third-Order ODEs with sl(2)	101; 7	Techniques Based on First Integrals	108; 	7.1	First Integrals Derived from Symmetries	108; 	7.2	Contact Symmetries and Dynamical Symmetries	116; 	7.3	Integrating Factors	122; 	7.4	Systems of ODEs	128; 8	How to Obtain Lie Point Symmetries of PDEs	136; 	8.1	Scalar PDEs with Two Dependent Variables	136; 	8.2	The Linearized Symmetry Condition for General PDEs	146; 	8.3	Finding Symmetries by Computer Algebra	149; 9	Methods for Obtaining Exact Solutions of PDEs	155; 	9.1	Group-Invariant Solutions	155; 	9.2	New Solutions from Known Ones	162; 	9.3	Nonclassical Symmetries	166; 10	Classification of Invariant Solutions	173; 	10.1	Equivalence of Invariant Solutions	173; 	10.2	How to Classify Symmetry Generators	176; 	10.3	Optimal Systems of Invariant Solutions	182; 11	Discrete Symmetries	187; 	11.1	Some Uses of Discrete Symmetries	187; 	11.2	How to Obtain Discrete Symmetries from Lie Symmetries	188; 	11.3	Classification of Discrete Symmetries	191; 	11.4	Examples	195; 	Hints and Partial Solutions to Some Exercises	201; 	Bibliography	209; 	Index	211
ER  -