He then assumed a post-doctoral position split between the Program in Applied and Computational Mathematics of Princeton University (10/2000–02/2001) and the Theoretical Division and the Center for Nonlinear Studies of Los Alamos National Laboratory (03/2001–08/2001).
These include a CAREER award in Applied Mathematics from the U.S. National Science Foundation (in 2003), a Humboldt Research Fellowship from the Humboldt Foundation, an Outstanding Paper Prize from the Society for Industrial and Applied Mathematics (SIAM), and the 2008 Stefanos Pnevmatikos International Award for research in nonlinear phenomena.
He was elected as a fellow of the Society for Industrial and Applied Mathematics in 2017, "for fundamental contributions to the existence, stability, and dynamics of nonlinear waves with applications to atomic, optical, and materials physics".
He published his third book in November 2013, an edited volume together with a number of his collaborators on Localized Excitations in Nonlinear Complex Systems: Current State of the Art and Future Perspectives, again by Springer-Verlag and his fourth book in 2014 with two co-editors on The sine-Gordon Model and its Applications: From Pendula and Josephson Junctions to Gravity and High Energy Physics.
As quantitative measures of his impact to the research community, one can mention the h-index of 42 (in Web of Science, 52 in Google Scholar) and that his work (excluding self-citations) has been cited over 5300 times.
He has worked with 5 post-doctoral research scholars; alumni of this group hold now permanent positions at the University of Essex in the UK, the CNRS in France, and Bowdoin College, among others.