vii §7.1. Isospectral Matrices 133 §7.2. Eigenfunctions and Differential Operators 138 §7.3. Dressing for Differential Operators 140 Problems 145 Suggested Reading 147 Chapter 8. Lax Form for KdV and Other Soliton Equations 149 §8.1. KdV in Lax Form 150 §8.2. Finding Other Soliton Equations 154 §8.3. Lax Equations Involving Matrices 159 §8.4. Connection to Algebraic Geometry 164 Problems 165 Suggested Reading 171 Chapter 9. The KP Equation and Bilinear KP Equation 173 §9.1. The KP Equation 173 §9.2. The Bilinear KP Equation 181 Problems 193 Suggested Reading 195 Chapter 10. The Grassmann Cone Γ2,4 and the Bilinear KP Equation 197 §10.1. Wedge Products 197 §10.2. Decomposability and the Plu¨cker Relation 200 §10.3. The Grassmann Cone Γ2,4 as a Geometric Object 203 §10.4. Bilinear KP as a Plu¨cker Relation 204 §10.5. Geometric Objects Problems 215 Suggested Reading 217 Chapter 11. Pseudo-Differential Operators and the KP Hierarchy 219 §11.1. Motivation 219 §11.2. The Algebra of Pseudo-Differential Operators 220 Nonlinear PDEs Solution the of in Spaces 209

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