We study periodic travelling wave solutions of a derivative non-linear
Schrödinger equation and show the existence of infinitely many
families of semi-trivial solutions (Theorem 2). Each of the families constitutes
a branch of travelling waves corresponding to a non-zero integer called the
winding number. A sufficient condition for the orbital stability of travelling
waves on the branches with positive winding number is given in terms of the wave
speed and winding number of the solution (Theorem 3). Bifurcation points are
found on each semi-trivial branch of travelling wave solutions (Theorem 4), and
the qualitative, and approximately quantitative, orbitshapes of the bifurcated
solutions are given. The stability of the semi-trivial solutions under
subharmonic perturbations is studied in Theorem 6, and subharmonic bifurcations
are established in Theorem 7.
Publié le : 2010-07-15
Classification:
periodic travelling wave,
orbital stability,
derivative non-linear Schrödinger equation,
bifurcation.,
35A15,
35B35,
35Q55
@article{1280754420,
author = {Imamura, Kouya},
title = {Stability and bifurcation of periodic travelling waves in a derivative non-linear
Schr\"odinger equation},
journal = {Hiroshima Math. J.},
volume = {40},
number = {1},
year = {2010},
pages = { 185-203},
language = {en},
url = {http://dml.mathdoc.fr/item/1280754420}
}
Imamura, Kouya. Stability and bifurcation of periodic travelling waves in a derivative non-linear
Schrödinger equation. Hiroshima Math. J., Tome 40 (2010) no. 1, pp. 185-203. http://gdmltest.u-ga.fr/item/1280754420/