3 papers
math.AP2025
Infinite-order rogue waves that are small (but not small in )
Deniz Bilman, Peter D. Miller
General rogue waves of infinite order constitute a family of solutions of the focusing nonlinear Schrödinger equation that have recently been identified in a variety of asymptotic…
math.AP2025
Suleimanov-Talanov self-focusing and the hierarchy of the focusing nonlinear Schrödinger equation
Robert J. Buckingham, Robert M. Jenkins, Peter D. Miller
We study the self-focusing of wave packets from the point of view of the semiclassical focusing nonlinear Schrödinger equation. A type of finite-time collapse/blowup of the soluti…
math.CA2025
Rigorous Methods for Bohr-Sommerfeld Quantization Rules
Joanne Dong, Peter D. Miller, Giorgio Young
In this work, we prove Bohr-Sommerfeld quantization rules for the self-adjoint Zakharov-Shabat system and the Schrödinger equation in the presence of two simple turning points bou…