Projektnummer

0056333

Zusammenfassung

The purpose of this project is to investigate nonlinear evolution equations (e.g., nonlinear Schrodinger, Korteweg - de Vries and Sine-Gordon, etc.) with the boundary conditions given on metric graphs arising from mesoscopic physics and nanostructures. In particular, the initial and boundary-value problem and the property of transport through arbitrary graphs will be analyzed. Explicit solutions (including soliton solutions) will be obtained by considering certain topologies of graphs (e.g., star, tree, loop and other graphs). Different types of conservation laws will be derived for t...