Periodic rogue waves and perturbation theory

DOI10.1007/978-1-0716-2621-4_762zbMATH Open1548.37008MaRDI QIDQ6599410

Paolo Maria Santíni, Fabio Coppini, Petr G. Grinevich

Publication date: 6 September 2024

zbMATH Keywords

stabilityinstabilityintegrabilitysoliton equationsspectral curveLax pair

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton equations (35Q51) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

Cites Work

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• Modulation instability and periodic solutions of the nonlinear Schrödinger equation
• A soluble relativistic field theory
• The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains
• Modulation instability: The beginning
• Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation
• Exact first-order solutions of the nonlinear Schrödinger equation
• Exact integration of nonlinear Schrödinger equation
• The periodic problem for the Korteweg-de Vries equation
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Inverse problem for periodic finite-zoned potentials in the theory of scattering
• Hill's operator with finitely many gaps
• Note on the integration of Euler's equations of the dynamics of an \(n\)-dimensional rigid body
• Integrability and linear stability of nonlinear waves
• The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes
• Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case
• The Landau-Lifshitz equation, the NLS, and the magnetic rogue wave as a by-product of two colliding regular ``positons
• The Fermi-Pasta-Ulam problem. A status report
• Water waves, nonlinear Schrödinger equations and their solutions
• Analytic Properties of Bloch Waves and Wannier Functions
• Theta functions and non-linear equations
• Spectral theory of two-dimensional periodic operators and its applications
• On Homoclinic Structure and Numerically Induced Chaos for the Nonlinear Schrödinger Equation
• Nonlinear Dynamics of Deep-Water Gravity Waves
• Nonlinear differential−difference equations
• METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS
• The Perturbed Plane-Wave Solutions of the Cubic Schrödinger Equation
• Riemann Surfaces of Infinite Genus
• Method for Solving the Korteweg-deVries Equation
• The periodic Cauchy problem for PT-symmetric NLS, I: the first appearance of rogue waves, regular behavior or blow up at finite times
• On three-dimensional packets of surface waves
• Symbolic calculation in development of algorithms: split-step methods for the Gross–Pitaevskii equation
• The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes
• Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
• Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability
• The disintegration of wave trains on deep water Part 1. Theory
• Stabilizing the Benjamin–Feir instability
• The linear and nonlinear instability of the Akhmediev breather
• Long-time dynamics of the modulational instability of deep water waves
• Unsteady water wave modulations: Fully nonlinear solutions and comparison with the nonlinear Schrödinger equation.

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