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Title: Soliton equations and eigenvalue problems Speaker: Wen-Xiu Ma Time: 10:00am‐11:00am Place: PHY 120
We will discuss how to generate soliton equations as isospectral flows of eigenvalue problems on the Kac-Moody algebras. The zero curvature equation is the key tool in the general formulation.
Title: Hirota bilinear equations, Bell polynomials and linear superposition principles Speaker: Wen-Xiu Ma Time: 10:00am‐11:00am Place: PHY 120
We will discuss the linear superposition principle applying to Hirota bilinear equations, and show basic relations among Hirota bilinear equations, Bell polynomials and linear subspaces of solutions. The starting point to generate linear subspaces of solutions is resonance between different traveling waves.
Title: 2D Toda lattices and their bilinear Bäcklund transformations Speaker: Magdy Gamil Assad Time: 10:00am‐11:00am Place: PHY 120
We will discuss the Bäcklund transformation for (i) the Toda lattice equation and (ii) the Toda molecule equation. We will also check how we can use the \(\{L1,L2\}\) to present the 2D Toda equation. We will take a look at the modified Toda equation and Miura transformation as well.
Title: Bäcklund transformations for KP- and BKP-type bilinear equations Speaker: Alrazi Abdeljabbar Time: 10:00am‐11:00am Place: PHY 120
Using bi-linear techniques, Bäcklund transformations for the KP, BKP, modified BKP equations are generated.
Title: Bäcklund transformations for KdV-type bilinear equations Speaker: Yaning Tang, Northwest Polytechnic University P.R. China Time: 10:00am‐11:00am Place: PHY 120
Following a rule that a Bäcklund transformation in bilinear form corresponds to an exchange formula for the \(D\)-operator, we look for a Bäcklund transformation for the KdV equation and demonstrate that such Bäcklund transformations generate: (i) Lax pairs used in the inverse scattering method, (ii) new soliton equations, and (iii) Miura transformations. Some applications are illustrated.