コロキウム

Bifurcations and Spectral Stability of Solitary Waves in Nonlinear Wave Equations

山添祥太郎 氏

2020年9月3日(木) 15時00分

Zoom会議

In this talk, we consider two types of nonlinear wave equations, and develop theories based on dynamical systems approaches for bifurcations and spectral stability of solitary waves. In the first half, we study relative equilibria in symmetry breaking perturbations of infinite-dimensional Hamiltonian systems, as which solitary waves in many partial differential equations are frequently treated, and apply the theoretical results to solitary waves in the nonlinear Schrödinger equation with cubic nonlinearity and a small potential. In the second half, we study a wide class of coupled nonlinear Schrödinger equations and apply the theoretical results to a cubic nonlinearity case. For the examples given in both parts, we also present numerical results to demonstrate the validity and usefulness of the developed theories.

Last modified: Wed Jan 16 18:03:30 JST 2019