Nonlinear Waves Seminar - Jianke Yang

Jianke Yang, Department of Mathematics and Statistics, University of Vermont Wave Patterns in Higher-Order KP-I Lumps The Kadomtsev-Petviashvili-I (KP-I) equation models two-dimensional shallow water waves under strong surface tension as well as the evolution of weakly nonlinear two-dimensional plasma waves. In this talk, pattern formation in higher-order lumps of the KP-I equation at large times is analytically studied. For these higher-order lumps under certain internal-parameter restrictions, we show that the large-time wave patterns comprise fundamental lumps arranged in non-triangular shapes in the outer region, which are described analytically by nonzero-root structures of the Wronskian-Hermit polynomials, together with fundamental lumps arranged in triangular shapes in the inner region, which are described analytically by root structures of the Yablonskii-Vorob'ev polynomials. When time evolves from large negative to large positive, the non-triangular pattern in the outer region...