Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons

DOI10.1080/09500341003624750zbMath1203.78042OpenAlexW2063659812MaRDI QIDQ3064657

T. L. Belyaeva, V. N. Serkin, Akira Hasegawa

Publication date: 22 December 2010

Published in: Journal of Modern Optics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/09500341003624750

zbMATH Keywords

nonautonomous solitonsdispersion and nonlinearity variationsnonlinear Schrödinger equation with linear and harmonic oscillator potentialsSatsuma-Yajima breather

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Quantum equilibrium statistical mechanics (general) (82B10) Lasers, masers, optical bistability, nonlinear optics (78A60) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Topological dynamics of nonautonomous systems (37B55)

Related Items (32)

Lax pair, conservation laws, Darboux transformation, breathers and rogue waves for the coupled nonautonomous nonlinear Schrödinger system in an inhomogeneous plasma ⋮ Soliton control with inhomogeneous dispersion under the influence of tunable external harmonic potential ⋮ Chirped self-similar solitary waves in optical fibers governed with self-frequency shift and varying parameters ⋮ Novel rogue waves in an inhomogenous nonlinear medium with external potentials ⋮ Nonautonomous superposed Akhmediev breather in water waves ⋮ Controllable behaviors of spatiotemporal breathers in a generalized variable-coefficient nonlinear Schrödinger model from arterial mechanics and optical fibers ⋮ Exact \(N\)-soliton solutions and dynamics of a new AKNS equation with time-dependent coefficients ⋮ Lax integrability and exact solutions of a variable-coefficient and nonisospectral AKNS hierarchy ⋮ Exact Solutions of Nonlinear Equations in Mathematical Physics via Negative Power Expansion Method ⋮ The weakly nonlinear wave propagation of the generalized third-order nonlinear Schrödinger equation and its applications ⋮ Lax integrability and soliton solutions for a nonisospectral integrodifferential system ⋮ Nonautonomous solitons for an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma ⋮ On a generalized Ablowitz–Kaup–Newell–Segur hierarchy in inhomogeneities of media: soliton solutions and wave propagation influenced from coefficient functions and scattering data ⋮ Binary Darboux transformation and multi-dark solitons for a higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber ⋮ Nonlinear coherent states and Ehrenfest time for Schrödinger equation ⋮ Periodic and solitary waves generating in optical fiber amplifiers and fiber lasers with distributed parameters ⋮ Controllable behavior of self-similar matter waves in exotic transient trap variations ⋮ Symbiotic multimode spatial similaritons and rogons in inhomogeneously coupled optical fibers ⋮ Chirped double-kink and fractional-transform solitons in an optical gain medium with two-photon absorption ⋮ Multi-soliton solutions of the forced variable-coefficient extended Korteweg-de Vries equation arisen in fluid dynamics of internal solitary waves ⋮ Parametrically driven localized magnetic excitations with spatial inhomogeneity ⋮ Nonautonomous bright soliton solutions on continuous wave and cnoidal wave backgrounds in blood vessels ⋮ Effect of third-order dispersion on the solitonic solutions of the Schrödinger equations with cubic nonlinearity ⋮ Solitons in lattice field theories via tight-binding supersymmetry ⋮ Perturbation theory for Bose–Einstein condensates on bounded space domains ⋮ Modulation of localized solutions in quadratic-cubic nonlinear Schrödinger equation with inhomogeneous coefficients ⋮ Nonautonomous matter wave bright solitons in a quasi-1D Bose-Einstein condensate system with contact repulsion and dipole-dipole attraction ⋮ Solitary and extended waves in the generalized sinh-Gordon equation with a variable coefficient ⋮ MODULATION INSTABILITY AND OPTICAL SOLITONS OF RADHAKRISHNAN-KUNDU-LAKSHMANAN MODEL ⋮ Non-autonomous solitons in inhomogeneous nonlinear media with distributed dispersion ⋮ Matter rogue waves and management by external potentials for coupled Gross-Pitaevskii equation ⋮ Stability and instability of breathers in the U(1) Sasa–Satsuma and nonlinear Schrödinger models*

Cites Work

• Integrability of the Gross-Pitaevskii equation with Feshbach resonance management
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Darboux invariants of integrable equations with variable spectral parameters
• Beyond the spatio-temporal model in femtosecond optics
• EXACT BRIGHT SELF-SIMILAR SOLITARY WAVES IN AN EXPULSIVE PARABOLIC POTENTIAL
• Integrals of nonlinear equations of evolution and solitary waves
• Fermi–Pasta–Ulam, solitons and the fabric of nonlinear and computational science: History, synergetics, and visiometrics

This page was built for publication: Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons