A Short Primer on the Half-Wave Maps Equation
Lenzmann, Enno1
1 University of Basel Department of Mathematics Spiegelgasse 1, CH-4051 Basel Switzerland
Journées équations aux dérivées partielles (2018), Exposé no. 4, 12 p.

We review the current state of results about the half-wave maps equation on the domain ℝ d with target 𝕊 2 . In particular, we focus on the energy-critical case d=1, where we discuss the classification of traveling solitary waves and a Lax pair structure together with its implications (e.g. invariance of rational solutions and infinitely many conservation laws on a scale of homogeneous Besov spaces). Furthermore, we also comment on the one-dimensional space-periodic case. Finally, we list some open problem for future research.

Publié le :
DOI : 10.5802/jedp.664
Lenzmann, Enno 1

1 University of Basel Department of Mathematics Spiegelgasse 1, CH-4051 Basel Switzerland 
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Lenzmann, Enno. A Short Primer on the Half-Wave Maps Equation. Journées équations aux dérivées partielles (2018), Exposé no. 4, 12 p. doi : 10.5802/jedp.664. http://www.numdam.org/articles/10.5802/jedp.664/

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