\(1+1\) wave maps into symmetric spaces. (English) Zbl 1082.37068

Using Bäcklund transformations, the authors construct \(2k\)-soliton breather solutions for the -1 flow associated to a compact Lie group. They show how these give rise to \(2k\)-soliton homoclinic wave maps from the Lorentzian surface \(S^1\times \mathbb R^1\) into homogeneous spaces (where by wave maps the authors denote harmonic maps defined on a Lorentzian manifold). This result generalizes the result by J. Shatah and W. Strauss [Physica D 99, 113–133 (1996; Zbl 0890.58009)] according to which the classical breather solutions of the sine-Gordon equation give rise to periodic homoclinic wave maps into \(S^2= \text{SU}(2)/ \text{SO}(2)\).


37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems


Zbl 0890.58009
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