Standing waves of nonlinear Schrödinger systems with all attractive forces
Jaeyoung Byeon
Source abstract
Abstract Since the pioneering work of Lin and Wei on nonlinear Schrödinger systems of components with interaction forces between the ‐th and ‐th components for , there have been numerous further developments in many directions. However, even in the simplest case where all interaction forces are attractive, (which corresponds to for every ), a systematic approach to finding a solution with all positive components is still not known. In the special case , a very systematic approach has been developed by Ambrosetti and Colorado. In this paper, we review the fundamental works by Lin–Wei and Ambrosetti–Colorado and further developments.
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