Soliton-radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation

DOI10.1016/S0167-2789(02)00358-5zbMath1002.35112arXivnlin/0111034OpenAlexW2038509242MaRDI QIDQ5959700

Igor V. Barashenkov, Valery S. Shchesnovich

Publication date: 9 April 2002

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

Full work available at URL: https://arxiv.org/abs/nlin/0111034

zbMATH Keywords

Riemann-Hilbert problemfour-dimensional dynamical systeminteraction of the soliton with radiationlong-wavelength radiation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (10)

Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered states ⋮ A quasi-periodic route to chaos in a parametrically driven nonlinear medium ⋮ \(N\)-(soliton, breather) interactions for general multi-component third-fifth-order mKdV equations via Riemann-Hilbert method ⋮ Riemann-Hilbert approach and \(N\)-soliton solutions for a new two-component Sasa-Satsuma equation ⋮ Damped solitary waves on a superfluid vortex filament ⋮ Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces ⋮ Soliton pair interaction law in parametrically driven Newtonian fluid ⋮ Exponential integrators based on discrete gradients for linearly damped/driven Poisson systems ⋮ Riemann-Hilbert approach of the Newell-type long-wave-short-wave equation via the temporal-part spectral analysis ⋮ Interactions of fractional \(N\)-solitons with anomalous dispersions for the integrable combined fractional higher-order mKdV hierarchy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Breather dynamics in the nonlinear Schrödinger regime of perturbed sine-Gordon systems
• Faraday resonance: asymptotic theory of surface waves
• Topography of attractors of the parametrically driven nonlinear Schrödinger equation
• Low-dimensional chaos in a driven damped nonlinear Schrödinger equation
• The center manifold and bifurcations of damped and driven sine-Gordon breathers
• Perturbation theory for the modified nonlinear Schrödinger solitons
• A quasi-periodic route to chaos in a near-integrable PDE
• Parametrically excited solitary waves
• Nonlinear dynamics of two-mode interactions in parametric excitation of surface waves
• Faraday resonance in rectangular geometry
• On higher-order corrections in soliton perturbation theory
• Perturbations of Solitons and Solitary Waves
• Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability
• Parametrically Amplified 2-Dimensional Solitary Waves
• On localized solutions in nonlinear Faraday resonance

This page was built for publication: Soliton-radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation