On solutions
and lump wave patterns
of the (2+1)-dimensional
Yu-Toda-Sasa-Fukuyama equation
报告专家：虞国富 教授 （上海交通大学）
报告时间：7月30日（周三） 10:00--11:00
报告地点：国家天元数学西南中心401
报告摘要：
In this talk, we employ Hirota's bilinear technique to derive soliton, breather, and lump solutions to the (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation. These solutions are explicitly constructed as $N\times N$ Gram-type determinant expressions. A systematic analysis is conducted on the dynamical behaviors of one-, two-, and three-soliton configurations, breather structures, and lump solutions, including their propagation patterns and interaction mechanisms.
Furthermore, we investigate the hybrid interactions between breathers and solitons, revealing distinct collision dynamics governed by the underlying nonlinear dynamics. By strategically selecting parametric configurations, three distinct classes of breather solutions are identified: Akhmediev breathers, Kuznetsov-Ma breathers, and generalized breathers propagating along arbitrary oblique trajectories. These solutions are distinguished by their spatiotemporal periodicity and spectral properties. Lump solutions are formulated in terms of Schur polynomials. A novel link is established between the theory of integer partitions and the construction of multi-lump solutions, providing combinatorial insights into their algebraic structure. The geometric patterns emerging from these solutions are systematically characterized via the complex root configurations of special polynomials, such as the Yablonskii-Vorob'ev polynomials.
专家简介：
虞国富，上海交通大学数学科学学院教授、副院长、博士生导师。2007年博士毕业于中国科学院数学与系统科学研究院，加拿大蒙特利尔大学博士后，香港科技大学访问学者。主要从事可积系统、随机矩阵、正交多项式等相关领域的研究。在数学物理领域知名学术刊物Adv. Math., Ann. Henri Poincaré，Nonlinearity, JNS 等发表SCI论文60余篇。主持国家自然科学基金、上海市东方英才、上海交通大学晨星青年学者奖励计划等多项研究课题。
邀请人：李世豪
