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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 solutio…
math.AP2024
General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective numerical computation
Deniz Bilman, Peter D. Miller
This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schrödinger equation called general rogue waves of infinite order. These soluti…