Stability of multi-solitons in the cubic NLS equation

DOI10.1142/S0219891614500106zbMath1298.35190arXiv1307.2975OpenAlexW2106686547WikidataQ115245227 ScholiaQ115245227MaRDI QIDQ3190177

Andres Contreras, Dmitry E. Pelinovsky

Publication date: 16 September 2014

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.2975

zbMATH Keywords

inverse scattering transformorbital stabilitycubic nonlinear Schrödinger equationmulti-solitondressing transformation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items

Linear instability of breathers for the focusing nonlinear Schrödinger equation ⋮ Rogue periodic waves of the focusing nonlinear Schrödinger equation ⋮ Rogue periodic waves of the modified KdV equation ⋮ Asymptotic stability of N-solitons in the cubic NLS equation ⋮ Linear stability of elastic 2-line solitons for the KP-II equation ⋮ On asymptotic stability of multi-solitons for the focusing modified Korteweg-de Vries equation ⋮ Inverse Scattering for the Massive Thirring Model ⋮ Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity ⋮ L²orbital stability of Dirac solitons in the massive Thirring model ⋮ On asymptotic stability of nonlinear waves

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic stability of lattice solitons in the energy space
• Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation
• Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model
• Stability theory of solitary waves in the presence of symmetry. I
• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• Asymptotic stability of \(N\)-solitary waves of the FPU lattices
• Slow solution interaction with delta imperiums
• Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
• Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations
• On the stability ofN-solitons in integrable systems
• L2-Sobolev space bijectivity of the scattering and inverse scattering transforms
• Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space
• PHASE-DRIVEN INTERACTION OF WIDELY SEPARATED NONLINEAR SCHRÖDINGER SOLITONS
• The Gardner equation and the 𝐿²-stability of the 𝑁-soliton solution of the Korteweg-de Vries equation
• The asymptotic stability of solitons in the cubic NLS equation on the line