Index Adjoint operator, 221, 222 Benjamin Equation, 19 Solitary waves, 28 Stability of solitary waves, 129 Benjamin-Ono Equation, 18 Generalized, 18 Local well-posedness, 51 Periodic travelling wave solutions, 12, 39 Regularized, 22 Solitary waves, 27 Stability of periodic waves, 192 Stability of solitary waves, 98, 124 Benjamin-type equations, 127 Benney-Luke Cnoidal waves, 177 Equation, 177 Stability of cnoidal waves, 182 Blow up, 51, 70, 137, 195 Bourgain spaces, 52 Boussinesq Equation, 102 Systems, 22 Class PF(2), 99 Class PF(2) discrete, 185, 192 Cnoidal wave, 10, 31, 35, 161, 164, 177, 188, 197, 209 Complementary modulus, 208 Complete Elliptic integral of the first kind, 208 Elliptic integral of the second kind, 208 Concentration-Compactness method, 7, 106, 125, 127 Critical Korteweg-de Vries Equation, 37 Instability of periodic waves, 193 Periodic travelling wave solutions, 37 Solitary waves, 27 Stability of periodic waves, 193 Critical Nonlinear Schr¨ odinger Equation, 137, 164, 194 Instability of periodic waves, 195 Periodic travelling wave solutions, 194 Stability of periodic waves, 195 Critical solitary wave, 157 DispersiveWiki project, 49 Dnoidal wave, 10, 34, 41, 209 Duality, 206 Duhamel formula, 50 Embedding, 52 Floquet theory, 240 Fourier coeﬃcient, 190 Fourier transform, 188, 201, 202, 203, 206 Gagliardo-Nirenberg-type inequality, 82, 125 Gear and Grimshaw system, 22, 157 Group, 50, 142 Hilbert transform, 203 Hypergeometric differential equation, 209 Instability Intervals, 241 Linear, 153 Orbital, 63 Instability for the generalized Benjamin equation, 139, 143 Instability for the generalized Korteweg-de Vries equation, 138, 150 Instability for weakly coupled KdV systems, 154 Intermediate long wave Equation, 18 Solitary waves, 28 Stability of solitary waves, 100 Jacobi form of Lam´ e’s equation, 10, 162, 242 Jacobian elliptic functions, 210 Kadomtsev-Petviashvili-I Equation, 20 Generalized, 20 255

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