Local existence of a fourth-order dispersive curve flow on locally Hermitian symmetric spaces and its application

DOI10.1016/j.difgeo.2019.101560zbMath1425.53086arXiv1606.04664OpenAlexW2972913373WikidataQ115354892 ScholiaQ115354892MaRDI QIDQ2328004

Eiji Onodera

Publication date: 8 October 2019

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.04664

zbMATH Keywords

energy methodloss of derivativesbi-Schrödinger flowlocally Hermitian symmetric spacefourth-order dispersive partial differential equationtime-local existence

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Initial-boundary value problems for systems of nonlinear higher-order PDEs (35G61)

Related Items (2)

On the vortex filament in 3-spaces and its generalizations ⋮ Uniqueness Of 1D generalized bi-Schrödinger flow

Cites Work

• New geometric flows on Riemannian manifolds and applications to Schrödinger-Airy flows
• Vortex filament on symmetric Lie algebras and generalized bi-Schrödinger flows
• On the global well-posedness of the one-dimensional Schrödinger map flow
• Periodic weak solutions for a classical one-dimensional isotropic biquadratic Heisenberg spin chain
• Generalized Hasimoto transform of one-dimensional dispersive flows into compact Riemann surfaces
• A third-order dispersive flow for closed curves into Kähler manifolds
• The Cauchy problem for Schrödinger flows into Kähler manifolds
• A third order dispersive flow for closed curves into almost Hermitian manifolds
• Schrödinger flow of maps into symplectic manifolds
• The vortex filament equation and a semilinear Schrödinger equation in a Hermitian symmetric space
• Solvability of equations for motion of a vortex filament with or without axial flow
• Local Schrödinger flow into Kähler manifolds
• A fourth-order dispersive flow equation for closed curves on compact Riemann surfaces
• Geometric Schrödinger-Airy flows on Kähler manifolds
• The Cauchy problem of generalized Landau-Lifshitz equation into \(S ^{n }\)
• A fourth-order dispersive flow into Kähler manifolds
• Fourth-order dispersive systems on the one-dimensional torus
• A Curve Flow on an Almost Hermitian Manifold Evolved by a Third Order Dispersive Equation
• Some Geometric Flows on Kahler Manifolds
• GEOMETRIC KdV FLOWS, MOTIONS OF CURVES AND THE THIRD-ORDER SYSTEM OF THE AKNS HIERARCHY
• KdV GEOMETRIC FLOWS ON KÄHLER MANIFOLDS
• The KdV curve and Schrödinger-Airy curve
• The Initial Value Problem for Third and Fourth Order Dispersive Equations in One Space Dimension
• An Approximation Scheme for Schrödinger Maps
• 2-harmonic maps and their first and second variational formulas
• Schrödinger maps
• Motion and expansion of a viscous vortex ring. Part 1. A higher-order asymptotic formula for the velocity
• The initial-value problem for a fourth-order dispersive closed curve flow on the 2-sphere
• Initial and Initial-Boundary Value Problems for a Vortex Filament with or without Axial Flow
• Schrödinger flow into almost Hermitian manifolds
• Geometric solitons of Hamiltonian flows on manifolds
• Schrodinger Maps and their Associated Frame Systems
• Harmonic Mappings of Riemannian Manifolds
• Three-dimensional distortions of a vortex filament with axial velocity

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