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I am studying the following paper.

Manoussos Grillakis, Jalal Shatah, and Walter Strauss, Stability theory of solitary waves in the presence of symmetry. I, J. Funct. Anal. 74 (1987), no. 1, 160–197.

This is a highly cited paper that has given rise to a lot of Mathematics. But as beginner I am finding it hard to appreciate the the abstract mechanisms in their proof and their result. My question is can somebody provide me some papers where they used the results of GSS in some concrete situations?. I know that they discuss some applications at the back end of their paper. I am asking can I find more?. I hope my question is appropriate here.

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    $\begingroup$ I suggest changing the title so that it doesn't sound like you are asking for opinions about the paper. Asking for opinions sounds off-topic, but asking for applications of a paper sounds on-topic. $\endgroup$
    – Joonas Ilmavirta
    Commented Oct 26, 2014 at 22:20

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Maybe the following review article http://www.ams.org/journals/bull/2009-46-01/S0273-0979-08-01228-7/home.html (Why are solitons stable? by Terence Tao) will be helpful.

Some applications of the soliton stability theory to problems in plasma physics and hydrodynamics are considered in another (however, somewhat old) review article http://www.sciencedirect.com/science/article/pii/0370157386900165 (Soliton stability in plasmas and hydrodynamics, by E.A. Kuznetsov, A.M. Rubenchik and V.E. Zakharov).

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