Dark–dark and dark–bright soliton interactions in the two-component defocusing nonlinear Schrödinger equation

DOI10.1080/00036811.2011.618126zbMath1283.37066OpenAlexW1971838862WikidataQ58159252 ScholiaQ58159252MaRDI QIDQ4908202

Garrett Dean, Federica Vitale, Taylor Klotz, Barbara Prinari

Publication date: 4 March 2013

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2011.618126

zbMATH Keywords

inverse scattering transformsolitonsinteractionnonlinear Schrödinger systemsbright solitondark soliton

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Related Items (8)

Manakov system with parity symmetry on nonzero background and associated boundary value problems ⋮ Non-classical symmetry and analytic self-similar solutions for a non-homogenous time-fractional vector NLS system ⋮ Bright-dark and dark-dark solitons in coupled nonlinear Schrödinger equation with PT-symmetric potentials ⋮ Inverse scattering transform for nonlinear Schrödinger systems on a nontrivial background: a survey of classical results, new developments and future directions ⋮ Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations ⋮ Three-wave resonant interactions: multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics ⋮ Multiple bright and dark soliton solutions in three component spinor Bose-Einstein condensates ⋮ Dark-bright soliton solutions with nontrivial polarization interactions for the three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions

Cites Work

• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Inverse Scattering Method for the Nonlinear Evolution Equations under Nonvanishing Conditions
• Inverse Scattering Transform for the Multi-Component Nonlinear Schrödinger Equation with Nonzero Boundary Conditions
• Symmetries for exact solutions to the nonlinear Schrödinger equation
• Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions
• Solitons, boundary value problems and a nonlinear method of images
• The Dirac inverse spectral transform: Kinks and boomerons
• Non-self-adjoint Zakharov–Shabat operator with a potential of the finite asymptotic values. I. Direct spectral and scattering problems
• Bright and dark soliton solutions to coupled nonlinear Schrodinger equations

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