Novel solution of the system describing the resonant interaction of three waves

DOI10.1016/j.physd.2004.11.007zbMath1062.37064OpenAlexW2048666467MaRDI QIDQ1765730

Antonio Degasperis, Francesco Calogero

Publication date: 23 February 2005

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2004.11.007

zbMATH Keywords

time evolutionboomeronsemi-dark single solitontrappon

Mathematics Subject Classification ID

Related Items (10)

Isochronous and partially isochronous Hamiltonian systems are not rare ⋮ A Riemann-Hilbert approach in the form of a block matrix for the coupled matrix integrable system ⋮ The 3-wave resonant interaction model: spectra and instabilities of plane waves ⋮ Three-wave resonant interactions: multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics ⋮ Resonant solitons from the \(3 \times 3\) operator ⋮ The three-wave resonant interaction equations: Spectral and numerical methods ⋮ Exact solutions of the 3-wave resonant interaction equation ⋮ On isochronous Shabat-Yamilov-Toda lattices: equilibrium configurations, behavior in their neighborhood, Diophantine relations and conjectures ⋮ Modulational instability of dark solitons in three wave resonant interaction ⋮ Darboux transformation and novel solutions for the long wave-short wave model

Cites Work

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• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Exact solutions of the 3-wave resonant interaction equation
• Universality and integrability of the nonlinear evolution PDE’s describing N-wave interactions
• New Integrable Equations of Nonlinear Schrodinger Type
• Periodic Motions Galore: How to Modify Nonlinear Evolution Equations so that They Feature a Lot of Periodic Solutions
• New integrable PDEs of boomeronic type

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