### CAS Seminar

# Anton Kutsenko

### (Jacobs University)

## "Waves and integral continued fractions"

** Date: ** |
Wed, September 6, 2017 |

** Time: ** |
14:15 |

** Place: ** |
Research I Seminar Room |

**Abstract:** We consider a wave propagation in uniform or periodic structures with various defects. We discuss the following questions:

- What are guided, local waves and their dispersion diagrams?
- How to rewrite finite-difference wave equations in terms of integral operators?
- How to solve these integral equations and find the spectra explicitly, by using integral continued fractions?

As an application, we show that the probability of existence of local waves in the uniform lattice with one simple wave guide and one embedded point defect is \(3/4-1/(2\pi)\).