Soliton Dynamics in the Korteweg-de Vries (KdV) Equation with Step Boundary Conditions
Dr. Xudan Luo
State University of New York
About the Speaker
Dr. Luo received her PhD in Mathematics from Hong Kong University of Science and Technology in 2016. She was a postdoc at University of Colorado at Boulder; she is currently a postdoc at State University of New York at Buffalo. Her research interests include integrable systems, nonlinear waves, complex analysis and special functions.
The Korteweg-deVries equation with step type boundary conditions is reconsidered, with an emphasis on soliton dynamics. Solitons and continuous spectra are always present together. Solitons can pass through a step, in this case, the phase shift is calculated. Solitons can also become trapped, in this case, the corresponding eigenvalues of the Schrodinger equation are embedded in the continuous spectrum. The above results are confirmed numerically. For small dispersion, the above dynamics are described analytically.
All are welcome！