The 3-wave resonant interaction model: spectra and instabilities of plane waves

DOI10.1007/s00033-023-02104-8zbMath1528.37059OpenAlexW2986707441MaRDI QIDQ6053994

Sara Lombardo, Marzia Romano, Matteo Sommacal

Publication date: 24 October 2023

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-023-02104-8

zbMATH Keywords

stabilitymodulational instabilitytopological classificationthree wave resonant interaction model

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability in context of PDEs (35B35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Soliton equations (35Q51) Relationships between algebraic curves and integrable systems (14H70) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)

Cites Work

• The three-wave resonant interaction equations: Spectral and numerical methods
• Modulation instability: The beginning
• Integrability and linear stability of nonlinear waves
• Three-wave resonant interactions: multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics
• Novel solution of the system describing the resonant interaction of three waves
• Semiclassical soliton ensembles for the three-wave resonant interaction equations
• Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system
• The influence of modulational instability on energy exchange in coupled sine-Gordon equations
• Multicomponent integrable wave equations: I. Darboux-dressing transformation
• Wave Interactions and Fluid Flows
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems
• NONLINEAR SECOND SOUND WAVES IN SUPERFLUID HELIUM: INSTABILITIES, TURBULENCE AND ROGUE WAVES
• General rogue waves in the three-wave resonant interaction systems
• Ideals, Varieties, and Algorithms

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