On a coupled Kadomtsev--Petviashvili system associated with an elliptic curve
报告专家：傅蔚 副教授（华东师范大学）
报告时间：8月15日（周一）上午9:00-10:00
报告地点：腾讯会议：490 338 300（无密码）
摘要：
The coupled Kadomtsev--Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo and Miwa [J. Phys. Soc. Jpn., 52:766--771, 1983], is reinvestigated within the direct linearisation framework, which provides us with more insights into the integrability of this elliptic model from the perspective of a general linear integral equation. As a result, we successfully construct for the elliptic coupled Kadomtsev--Petviashvili system not only a Lax pair composed of differential operators in $2\times2$ matrix form but also multi-soliton solutions with phases parametrised by points on the elliptic curve. Dimensional reductions based on the direct linearisation, to the elliptic coupled Korteweg-de Vries and Boussinesq systems, are also discussed. In addition, a novel class of solutions are obtained for the $D_\infty$-type Kadomtsev--Petviashvili equation with nonzero constant background as a byproduct.
专家简介：
傅蔚，华东师范大学数学科学学院教师，本科与硕士毕业于上海大学数学系，2018年获利兹大学应用数学专业哲学博士学位。研究方向为可积系统，近年来主要从事可积微分与差分方程直接线性化理论的研究，相关结果发表在数学物理期刊《J. Math. Phys.》、《J. Phys. A》、《Nonlinearity》、《Proc. R. Soc. A》、《Stud. Appl. Math.》。主持完成上海市浦江人才计划项目，现主持国家自然科学基金青年项目。
