Initial Classification of Global Behavior Around Multi-Solitons for the Nonlinear Klein-Gordon Equation

Explore a mathematical talk on the nonlinear Klein-Gordon equation with focusing cubic power in three space dimensions. Delve into the classification of initial data for global behavior near multi-solitons generated from the ground state. Examine the challenges in tracing unstable modes of each soliton, considering their speed-dependent exponential growth rates. Investigate an ODE model suggesting potential disruption of growth rates and directions for slower modes due to indirect interactions. Discover the key mechanism of growth delay during energy transfer between solitons and learn about the crucial tool of energy estimates with exponential space-time weight for the linearized equation around multi-solitons. This 49-minute presentation, part of the Thematic Programme on "Nonlinear Waves and Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics, features joint work by Kenji Nakanishi and Gong Chen from Georgia Tech.