Table Of Content

Contents Preface Chapter 1. Theory of integrable systems Toda chain and nonlinear Schrodinger equation. Nonlocalities A.B. Shabat Huygens’ principle and integrable systems A.P. Veselov Linear operators with self-consistent coefficients and rational reductions of KP hierarchy I. Krichever Stationary flows: Hamiltonian structures and canonical transformations A.P. Fordy Classification of third order integrable evolution equations R.H. Heredero, VV. Sokolov and S.I. Svinolupov Numerical simulation of quasi-periodic solutions of the sine-Gordon equation M.J. Ablowitz, B.M. Herbst and M. Schober The new look on the theory of integrable systems A.N. Leznov Integrable deformations of a polygon V.E. Adler Generalized Hirota bilinear identity and integrable q-difference and lattice hierarchies L.V. Bogdanov Magnetic dipole in tunnel junction and solution of the boundary value problem by inverse scattering transform A.B. Borisov and VV. Kiseliev Nonintegrability of the Bianchi IX model A. Latifi, M. Musette and R. Conte Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations P.G. Grinevich and M.U. Schmidt The Davey—Stewartson equation and constrained linear flows F. Guil and M. Manas Additional symmetries for super KP hierarchies Manuel Manas, Luis Martinez Alonso and Elena Medina Reflectionless potentials and soliton series of the nonlinear Schrodinger equation V.Yu. Novokshenov On a structure of the explicit solutions to the Davey—Stewartson equations D. Pelinovsky Dressing of a two-dimensional nontrivial potential M. Boiti, F. Pempinelli and A. Pogrebkov Xil Contents Darboux transformations for “‘W-problems’”’ H. Steudel and R. Meinel Integrable boundary value problems for the multicomponent Schrodinger equations 1.T. Habibullin and S.1. Svinolupov Master symmetries for differential-difference equations of the Volterra type 1.Yu. Cherdantsev and R.I. Yamilov Chapter 2. Asymptotic and perturbative methods for integrable and near integrable models On a class of physically important integrable equations A.S. Fokas The nonlinear Schrodinger Hierarchy in perturbation theory A. Degasperis The variational principle for nonlinear waves in dissipative systems D.J. Kaup and B.A. Malomed Curved asymptotic solitons of Kadomtsev—Petviashvili-I and modified Kadomtsev—Petviashvili-I equations 1.A. Anders On the continuous Benney equations V.V. Geogjaev Asymptotic analysis of the Marchenko integral equation and soliton asymptotics of a solution of the nonlinear Schrodinger equation V.P. Kotlyarov Decay of an initial discontinuity in the defocusing NLS hydrodynamics G.A. El, VV. Geogjaev, A.V. Gurevich and A.L. Krylov Weak interaction of the KdV solitons under perturbation L.A. Kalyakin Chapter 3. Applications to nonlinear optics, fluid mechanics and plasma physics Nonlinear interaction of solitons and radiation E.A. Kuznetsov, A.V. Mikhailov and I.A. Shimokhin Phase diffusion and phase propagation: interesting connections A.C. Newell and Y. Pomeau Five-wave interaction on the surface of deep fluid A.I. Dyachenko, Y.V. Lvov and V.E. Zakharov All-optical-switching and pulse amplification and steering in nonlinear fiber arrays A.B. Aceves, C. De Angelis, G.G. Luther, A.M. Rubenchik and S.K. Turitsyn Sharper criteria for the wave collapse E.A. Kuznetsov, J.J. Rasmussen, K. Rypdal and S.K. Turitsyn Joint behavior of inertio-gravity and Rossby waves G. Falkovich, A. Shafarenko and G. Wilford “Explosive” evolution of galaxies (an analog of collapse) and appearance of quasars in the merger model V.M. Kontorovich, D.S. Krivitsky and A.V. Kats On Landau damping in models of Langmuir turbulence G.M. Fraiman and I.Yu. Kostyukov Contents Two-dimensional wave collapse in the boundary layer A.I. D’yachenko and E.A. Kuznetsov Topography of attractors of the parametrically driven nonlinear Schrédinger equation M. Bondila, I.V. Barashenkov and M.M. Bogdan The temperature-dependent collapse regime in a nonlinear dynamical model of Scheibe aggregates P.L. Christiansen, K.O. Rasmussen, O. Bang and Yu.B. Gaididei Long-term evolution of strong 2-D NSE turbulence G.M. Fraiman, E.M. Sher, A.D. Yunakovsky and W. Laedke Steady-state gas discharges in focused wave beams V.B. Gildenburg, T.A. Petrova and A.D. Yunakovsky Dynamics of fluid surface in multidimension N.A. Inogamov and S.I. Abarzhi Transformation of electromagnetic beams into surface waves on nonlinear interface A.V. Kochetov, A.G. Litvak, V.A. Mironov and E.M. Sher Raman spikes of pump repletion are not solitons C. Claude, F. Ginovart and J. Leon Modulational instability analysis of surface—waves in the Bénard—Marangoni phenomenon R.A. Kraenkel, M.A. Manna and J.G. Pereira All we know about hole solutions in the CGLE QO. Stiller, S. Popp, I. Aranson and L. Kramer Nonlinear Schrédinger models and modulational instability in real electrical lattices P. Marquié, J.M. Bilbault and M. Remoissenet Nonlinear theory of Kelvin-Helmholtz instability S.K. Zhdanov List of contributors