A unified inverse scattering transformation for the local and nonlocal nonautonomous Gross-Pitaevskii equations

DOI10.1063/1.4974772zbMath1362.37139OpenAlexW2582845213MaRDI QIDQ2963306

Wen-Xiu Ma, Dun Zhao, Yu-Juan Zhang

Publication date: 13 February 2017

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/97fe74e9dfa522ff6e82bf20817c485eeec8e324

zbMATH Keywords

AKNS hierarchyGross-Pitaevskii equationinverse scattering transformationinverse scattering solutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) 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) Soliton solutions (35C08)

Related Items (6)

The integrability conditions and solutions of nonautonomous Hirota equation ⋮ Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross–Pitaevskii Equation with Temporally and Spatially Modulated Coefficients ⋮ New dynamics of the classical and nonlocal Gross-Pitaevskii equation with a parabolic potential ⋮ Inverse scattering transformation and soliton stability for a nonlinear Gross-Pitaevskii equation with external potentials ⋮ Inverse scattering solutions and dynamics for a nonlocal nonlinear Gross-Pitaevskii equation with PT-symmetric external potentials ⋮ Solutions of solitary-wave for the variable-coefficient nonlinear Schrödinger equation with two power-law nonlinear terms

Cites Work

• Unnamed Item
• Unnamed Item
• Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation
• Integrable \(\mathcal{PT}\)-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation
• Energy-momentum transport through soliton in a site-dependent ferromagnet
• Soliton dispersion management in nonlinear optical fibers
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• Soliton Management in Periodic Systems
• Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Method for Solving the Korteweg-deVries Equation
• 𝓟𝓣-symmetric quantum mechanics
• AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schrödinger equations

This page was built for publication: A unified inverse scattering transformation for the local and nonlocal nonautonomous Gross-Pitaevskii equations