University at Buffalo · Department of Mathematics

MTH 839: Numerics for Nonlinear Waves

Fall 2026 · Weekly Schedule

Meetings: Monday and Wednesday, 12:30–1:50 p.m., Math 205

Instructor: Sergey A. Dyachenko

Email: sergeydy@buffalo.edu

Course page: MTH 839 Fall 2026

Recommended Textbooks

  1. Jianke Yang, Nonlinear Waves in Integrable and Nonintegrable Systems, SIAM, 2010.
  2. V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I: Wave Turbulence, Springer, 1992.

Weekly Schedule

The selection, sequence, and depth of topics may be adjusted as the course progresses.

Week Material
1 Petviashvili iteration.
2 Imaginary-time evolution method (ITEM).
3 Accelerated imaginary-time evolution method (Accelerated ITEM).
4 Squared-operator method; Newton--CG method.