Speaker: 柴雪冬博士，江苏师范大学

Title: Dbar Problems and Dynamics for the Nonlinear Evolution Equations

Language: Chinese

Time & Venue: 2025.07.22 14:00-15:00 腾讯会议：829-461-480

Abstract: We use the Dbar method to study the (2+1)-dimensional Jimbo-Miwa equation and the focusing Kundu-Eckhaus equation with non-zero boundary conditions, respectively. For the Jimbo-Miwa equation, a new Dbar problem is derived by means of the characteristic function and Green’s function of the Lax representation. The solution is constructed by combining the Cauchy-Green formula and appropriate spectral transformation, and the formal solution is obtained after determining the time evolution of the spectral data. For the focusing Kundu-Eckhaus equation, a Dbar problem with non-canonical normalization conditions at infinity is introduced. The Lax pair is constructed using eigenfunctions that are meromorphic outside the annulus. The original equation and conservation laws are derived by selecting a special distribution matrix. The N-soliton solutions are discussed based on symmetries and distributions, with the dynamic behaviors of the breather solutions analyzed as examples.