304 Index projective space, 286 pseudo-differential operators, viii, 219–221, 224, 225, 232, 298 quantum physics, 52, 53, 59, 60, 139 rogue waves, 281 Russell, John Scott, 45–50, 54, 55, 59, 62, 63 Sato, Mikio, 212, 248 Schr¨ odinger Operator, 53, 139, 145, 149, 150 shock wave, 38 SimpleEvolver[], 16 Simplify[], 262 Sine-Gordon Equation, 160, 169, 171 singular soliton, 99, 100, 284 singularity, 99, 100 Skyrme, T.H.R., 277 solitary wave, 46, 48, 50, 53–55, 58 soliton, 55, 56, 58, 89, 177 n-soliton, 56, 59, 60, 95, 96, 178, 284 interaction, 58, 103, 106 singular, 99, 100, 284 theory, ix, 60, 251, 253, 255 solution, differential equation, 2 Spectral Curve, 165 Sqrt[], 260 Stokes, George Gabriel, 47, 48, 51 superposition, 26, 31, 33, 40 symmetries, 66, 275 τ-function, 96, 99, 178, 181, 192, 194, 205, 206, 208, 209, 244 Table[], 98, 265 tau-function, see τ-function Toda Lattice, 161 translation, 19, 33, 46, 50 traveling wave, 32, 84 Tsingou, Mary, 53 Ulam, Stanislaw, 53, 54 viscosity, 39, 40 Wave Equation, 30, 32, 55, 64 wedge product, 197, 198, 235 Weierstrass p-function, see ℘- function WeierstrassHalfPeriods[], 73, 75 WeierstrassInvariants[], 76, 86, 179 WeierstrassP[], 72, 74, 75, 77, 86, 179 WeierstrassPPrime[], 72 Wronskian, 98, 127, 128, 132, 189, 192, 195, 204–208, 212, 216, 217, 230, 241, 245, 266, 267, 298 Wronskian[], 98 Wronskian Matrix, 128, 266 WronskianMatrix[], 266 Zabusky, Norman, 54, 277
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