Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)

DOI10.1090/bproc/116zbMath1493.37078OpenAlexW4220859331MaRDI QIDQ5030156

Wen-Xiu Ma

Publication date: 16 February 2022

Published in: Proceedings of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/bproc/116

zbMATH Keywords

Liouville integrabilityzero curvature equationintegrable reduction

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) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Related Items (17)

Nonlocal integrable mKdV equations by two nonlocal reductions and their soliton solutions ⋮ Reduced non-local integrable NLS hierarchies by pairs of local and non-local constraints ⋮ Reduced nonlocal integrable mKdV equations of type (−λ, λ) and their exact soliton solutions ⋮ Four-component integrable hierarchies and their Hamiltonian structures ⋮ Structures of interaction between lump, breather, rogue and periodic wave solutions for new \((3 + 1)\)-dimensional negative order KdV-CBS model ⋮ Integrable nonlocal nonlinear Schrödinger hierarchies of type \((-\lambda*,\lambda)\) and soliton solutions ⋮ Four-component integrable hierarchies of Hamiltonian equations with \((m+n+2)\)th-order Lax pairs ⋮ Dispersion-Managed Lump Waves in a Spatial Symmetric KP Model ⋮ The Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation, soliton interactions and position shift ⋮ Bifurcations and exact solutions of a new \((3+1)\)-dimensional Kadomtsev-Petviashvili equation ⋮ A family of solutions of the time–space fractional longitudinal wave equation ⋮ AKNS type reduced integrable bi-Hamiltonian hierarchies with four potentials ⋮ Soliton solutions to constrained nonlocal integrable nonlinear Schrödinger hierarchies of type (−λ,λ) ⋮ Topological degree for Chern-Simons Higgs models on finite graphs ⋮ Lump solution, breather soliton and more soliton solutions for a \((2 + 1)\)-dimensional generalized Benjamin-Ono equation ⋮ Bright and dark solitons and periodic wave solutions for the Gerdjikov-Ivanov equation in nonlinear fiber optics ⋮ A multi-component integrable hierarchy and its integrable reductions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable theory of the perturbation equations.
• A soliton hierarchy associated with \(\mathrm{so}(3,\mathbb R)\)
• Distinguished figures in mechanism and machine science. Their contributions and legacies. Part 1
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Enlarging spectral problems to construct integrable couplings of soliton equations
• New soliton hierarchies associated with the Lie algebra so(3,\(\mathbb{R}\)) and their Bi-Hamiltonian structures
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• New soliton hierarchies associated with the real Lie algebra so(4,R)
• COUPLING INTEGRABLE COUPLINGS
• On Liouville integrability of zero-curvature equations and the Yang hierarchy
• Application of hereditary symmetries to nonlinear evolution equations
• An exact solution for a derivative nonlinear Schrödinger equation
• A simple model of the integrable Hamiltonian equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• On Integrability of a (2+1)-Dimensional Perturbed KdV Equation
• Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies
• A spectral problem based on so$(3,\mathbb {R})$(3,R) and its associated commuting soliton equations
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
• Integrals of nonlinear equations of evolution and solitary waves

This page was built for publication: Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)