viii §11.3. ΨDOs are Not Really Operators 224 §11.4. Application to Soliton Theory 225 Problems 232 Suggested Reading 234 Chapter 12. The Grassmann Cone Γk,n and the Bilinear KP Hierarchy 235 §12.1. Higher Order Wedge Products 235 §12.2. The Bilinear KP Hierarchy 240 Problems 246 Suggested Reading 248 Chapter 13. Concluding Remarks 251 §13.1. Soliton Solutions and their Applications 251 §13.2. Algebro-Geometric Structure of Soliton Equations 252 Appendix A. Mathematica Guide 257 §A.1. Basic Input 257 §A.2. Some Notation 259 §A.3. Graphics 263 §A.4. Matrices and Vectors 265 §A.5. Trouble Shooting: Common Problems and Errors 267 Appendix B. Complex Numbers 269 §B.1. Algebra with Complex Numbers 269 §B.2. Geometry with Complex Numbers 270 §B.3. Functions and Complex Numbers 272 Problems 274 Appendix C. Ideas for Independent Projects 275 References 289 Glossary of Symbols 297 Index 301
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