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SUMMARY:Elliptic finite-band potentials of a non-self-adjoint Zakharov-Sha
 bat operator. - Xudan Luo (Chinese Academy of Sciences)
DTSTART:20221129T110000Z
DTEND:20221129T120000Z
UID:TALK193187@talks.cam.ac.uk
DESCRIPTION:The cubic nonlinear Schrodinger (NLS) equation is an integrabl
 e universal model that describes the evolution of slowly varying envelope 
 of a quasi-monochromatic wave in weakly nonlinear media. From both mathema
 tical and physical point of view\, the dynamics of self-focusing media gov
 erned by the focusing NLS equation with periodic boundary conditions has b
 een a classical research topic. In this talk\, we present a novel\, explic
 it two-parameter family of finite-band Jacobi elliptic potentials for the 
 non-self-adjoint Zakharov-Shabat operator\, which connects two previously 
 known limiting cases in which the elliptic parameter is zero or one. A ful
 l characterization of the spectrum and the connection problems for Heun&rs
 quo\;s equation are discussed.&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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