Index 303 Lax operator, 151, 160, 162, 220, 277 Lax Pair, see Lax operator Lax, Peter, 150 linear differential equation, 4, 23, 25, 26, 29, 30, 40 linear independence, 27, 109, 127, 129, 130, 207, 236, 237, 267, 286 maketau[], 98, 99 makeu[], 98, 99, 183 Mathematica, xi–xiii, xv, 13, 16, 17, 19, 20, 30, 37, 38, 64, 72–74, 76–78, 80, 85–87, 89, 92, 98, 99, 101, 103, 104, 110, 119– 121, 127–129, 143, 145– 147, 167, 168, 175, 176, 179, 182–184, 186–188, 191–195, 206, 207, 209, 210, 213, 214, 217, 233, 242, 244, 247, 257–268, 270, 272, 274, 278, 279, 281, 282, 284, 285 arithmetic, 259 capitalization, 267 complex numbers, 270 defining functions, 261 graphics, 263 making animations, 13 matrices and vectors, 265 numerical approximation, 263 simplifying expressions, 262 matrix exponentiation, 279 MatrixExp[], 279 method of characteristics, 36 Module[], 262 MyAnimate[], 13, 85, 174 N[], 263 n-KdV Hierarchy, 156, 168, 220, 226, 227, 231, 232 n-soliton, see soliton Navier-Stokes Equations, 38 nicely weighted functions, 170, 187–189, 191, 192, 194, 195, 204, 208, 212, 216, 217, 241–243, 245, 298 nonlinear differential equation, 4 Nonlinear Schr¨ odinger Equation, 277 Novikov, Sergei, 65 numerical approximation, 54, 280, 282 ocean waves, 178, 179 odoapply[], 119 odomult[], 119 odosimp[], 119–121 optical solitons, 63, 278 ordinary differential equation, 4 ℘-function, 71, 72, 74–77, 80, 84, 95, 179 ParametricPlot[], 77 partial differential equation, 4, 18, 51, 59, 61, 62, 89 Pasta, John, 53 Perring, J.K., 277 Petviashvili, V.I., 178 phase shift, 106, 107, 109, 111, 176 phi[], 188 Plot[], 263 Plot3D[], 264 Pl¨ ucker relations, 200, 202, 204, 206, 238, 239 potential function, 139, 150 projective space, 71
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