Bäcklund Transformations and Their Applications [1ST ed.] 0125928505, 9780125928502
309 19 3MB
English Pages iii-xiii, 1-334 [174] Year 1982
Table of contents :
Content:
Edited by
Page iii
Copyright page
Page iv
Dedication
Page v
Preface
Pages xi-xii
Acknowledgments
Page xiii
General Introduction and Outline
Pages 1-11
CHAPTER 1 Bäcklund Transformations and Their Application to Nonlinear Equations of Mathematical Physics
Pages 12-122
CHAPTER 2 A Local Jet-Bundle Formulation of Bäcklund Transformations
Pages 123-150
CHAPTER 3 Bäcklund Transformations in Gasdynamics, Nonlinear Heat Conduction, and Magnetogasdynamics
Pages 151-196
CHAPTER 4 Bäcklund Transformations and Wave Propagation in Nonlinear Elastic and Nonlinear Dielectric Media
Pages 197-237
CHAPTER 5 Bäcklund Transformations and Stress Distribution Theory in Elastostatics
Pages 238-273
APPENDIX I Properties of the Hirota Bilinear Operators
Pages 274-275
APPENDIX II Differential Forms
Pages 276-285
APPENDIX III Differential Forms on Jet Bundles
Pages 286-291
APPENDIX IV The Derivation of the Equations That Define Bk+1,1 (Ψ)
Pages 292-293
APPENDIX V Symmetries of Differential Equations and Exterior Systems
Pages 294-298
APPENDIX VI Composition of Symmetries and Bäcklund Maps
Pages 299-301
References
Pages 302-321
Author Index
Pages 323-328
Subject Index
Pages 329-334
Content:
Edited by
Page iii
Copyright page
Page iv
Dedication
Page v
Preface
Pages xi-xii
Acknowledgments
Page xiii
General Introduction and Outline
Pages 1-11
CHAPTER 1 Bäcklund Transformations and Their Application to Nonlinear Equations of Mathematical Physics
Pages 12-122
CHAPTER 2 A Local Jet-Bundle Formulation of Bäcklund Transformations
Pages 123-150
CHAPTER 3 Bäcklund Transformations in Gasdynamics, Nonlinear Heat Conduction, and Magnetogasdynamics
Pages 151-196
CHAPTER 4 Bäcklund Transformations and Wave Propagation in Nonlinear Elastic and Nonlinear Dielectric Media
Pages 197-237
CHAPTER 5 Bäcklund Transformations and Stress Distribution Theory in Elastostatics
Pages 238-273
APPENDIX I Properties of the Hirota Bilinear Operators
Pages 274-275
APPENDIX II Differential Forms
Pages 276-285
APPENDIX III Differential Forms on Jet Bundles
Pages 286-291
APPENDIX IV The Derivation of the Equations That Define Bk+1,1 (Ψ)
Pages 292-293
APPENDIX V Symmetries of Differential Equations and Exterior Systems
Pages 294-298
APPENDIX VI Composition of Symmetries and Bäcklund Maps
Pages 299-301
References
Pages 302-321
Author Index
Pages 323-328
Subject Index
Pages 329-334
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