302 Index factoring, 121, 132 kernel, 24, 27, 28 multiplication, 115, 118 dispersion, 35, 40, 48, 52 dressing, 131, 136, 140, 146, 152, 154, 174, 220, 228, 245, 252 eigenfunction, 138–140, 143, 144, 146, 147 elliptic curves, 50, 53, 68, 70, 77, 80, 89 group law, 82 singular, 69, 71 evolution equation, 15, 226, 228 Exp[], 260 Fermi, Enrico, 53 Fermi-Pasta-Ulam Experiment, 53, 54, 280 findK[], 128, 141, 143 Fourier Analysis, 32 gauge transformation, 185, 186, 194, 248 Gelfand-Levitan-Marchenko Inver- sion Formula, 150 Grassmann Cone, 200, 203, 204, 206, 209, 238, 253, 254 Grassmannian, 204, 205, 286 Great Eastern (The), 49 Hirota derivatives, 187, 283 Hirota, Ryogo, 187 initial profile, 13, 15–20, 23, 34, 36–38, 41, 51, 54, 86, 103, 157, 168 internal waves, 281 intertwining, 131, 134, 135, 140, 141, 143, 146, 166, 170, 278 invariant subspace, 140, 152, 166, 191 inverse scattering, 59, 150 inviscid, 40 Inviscid Burgers’ Equation, 51 Inviscid Burgers’ Equation, 36, 38 isospectrality, 134, 137, 144, 145, 149, 254 Jacobian, 90, 165, 254 Kadomtsev, B.B., 178 KdV[], 64, 99 KdV Equation, 51 KdV Equation, 50, 51, 54, 59, 62–64, 84, 85, 89, 95, 96, 106, 150, 154, 165, 173 rational solutions, 63 stationary solutions, 63 kernel, 24, 27, 28, 42, 122, 131, 132, 138, 140, 141, 143– 145, 166, 170, 225, 228– 230 Korteweg, Diederik, 50, 62 KP[], 175 KP Equation, 90, 173, 178, 181, 183, 191, 192, 228, 233, 285 rational solutions, 193, 195 KP Hierarchy, 227–231, 233, 244, 245 Kruskal, Martin, 54, 277 Lax Equation, 150, 152, 155, 158, 165, 219, 225, 226, 229, 252, 277
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