×

On the Darboux and Birkhoff steps in the asymptotic stability of solitons. (English) Zbl 1417.37254

Summary: We give a unified proof of the step to find Darboux coordinates and of the ensuing Birkhoff normal forms procedure, developed in the course of the proof of asymptotic stability of solitary waves for NLS and special cases of Nonlinear Dirac equations.

MSC:

37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q41 Time-dependent Schrödinger equations and Dirac equations
35Q55 NLS equations (nonlinear Schrödinger equations)
PDF BibTeX XML Cite
Full Text: arXiv