报告题目：Soliton and periodic wave interaction solutions for sine-Gordon-type equations
报告人：安红利 南京农业大学 副教授
报告摘要：By employing the Madelung transformation, the time-dependent harmonic oscillator with friction described by the Schr¨odinger equation is reduced to a hydrodynamic system. An exponential elliptic vortex ansatz is introduced and thereby a finite-dimensional nonlinear dynamical system is obtained. Time modulated physical variables corresponding to the divergence, spin, shear, and normal deformation rates of the Madelung velocity field are introduced and the dynamical system is reducible to a form amenable to general solutions. In particular, three typical elliptical vortex solutions termed pulsrodons are derived and their behaviors are simulated. These solutions have recently found applications in oceanic and atmospheric dynamics. Moreover, it is shown that the harmonic oscillator with friction has an underlying integrable structure of Ermakov-Hamiltonian type.