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Elliptic finite-band potentials of a non-self-adjoint Zakharov-Shabat operator.

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

The cubic nonlinear Schrodinger (NLS) equation is an integrable universal model that describes the evolution of slowly varying envelope of a quasi-monochromatic wave in weakly nonlinear media. From both mathematical and physical point of view, the dynamics of self-focusing media governed by the focusing NLS equation with periodic boundary conditions has been a classical research topic. In this talk, we present a novel, explicit 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 full characterization of the spectrum and the connection problems for Heun’s equation are discussed. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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