Semigroup estimates and stability/instability results for the linearized three waves interaction equations

DOI10.1007/s13163-011-0070-yzbMath1291.35033OpenAlexW2029278128MaRDI QIDQ365127

David Chiron

Publication date: 4 September 2013

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13163-011-0070-y

zbMATH Keywords

stabilityeigenvaluesemigrouppump-wave approximationthree waves interaction equations

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Nonlinear first-order PDEs (35F20) Linear first-order PDEs (35F05) Initial-boundary value problems for systems of nonlinear first-order PDEs (35F61)

Cites Work

• The inverse scattering solution for the full three dimensional three-wave resonant interaction
• Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances
• Travelling waves for the nonlinear Schrödinger equation with general nonlinearity in dimension one
• Direct and inverse scattering transforms with arbitrary spectral singularities
• Inverse scattering and evolution equations
• Wave Interactions and Fluid Flows
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• L2-Sobolev space bijectivity of the scattering and inverse scattering transforms
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