skip to main content

Title: Geometric solitons of Hamiltonian flows on manifolds

It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Authors:
 [1] ;  [2] ;  [3]
  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China)
  2. School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China)
  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
Publication Date:
OSTI Identifier:
22250948
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; GEODESICS; GEOMETRY; HAMILTONIANS; MATHEMATICAL SOLUTIONS; SOLITONS; SPACE; SURFACES