TY - JOUR
T1 - Circular viewpoint of higher-order rogue wave structures of the nonlinear Schrödinger equation
AU - Ankiewicz, A.
N1 - Publisher Copyright:
© 2025 The Author(s). Published by IOP Publishing Ltd.
PY - 2025/4/1
Y1 - 2025/4/1
N2 - We analyze rogue wave patterns for various orders of the nonlinear Schrödinger equation for large values of solution parameters. We use a combination of exact solutions, geometric constructions and polynomial approximations for analysis, and introduce a new way of viewing the formations of rogue waves, including the triangular ones, by showing that they all can be represented as occupying circular shells, some of which contain ‘nuclei’.
AB - We analyze rogue wave patterns for various orders of the nonlinear Schrödinger equation for large values of solution parameters. We use a combination of exact solutions, geometric constructions and polynomial approximations for analysis, and introduce a new way of viewing the formations of rogue waves, including the triangular ones, by showing that they all can be represented as occupying circular shells, some of which contain ‘nuclei’.
KW - circular viewpoint
KW - higher-order rogue waves
KW - nonlinear schrödinger equation
KW - nonlinear structures
UR - http://www.scopus.com/inward/record.url?scp=86000316821&partnerID=8YFLogxK
U2 - 10.1088/1402-4896/adb79c
DO - 10.1088/1402-4896/adb79c
M3 - Article
AN - SCOPUS:86000316821
SN - 0031-8949
VL - 100
JO - Physica Scripta
JF - Physica Scripta
IS - 4
M1 - 045204
ER -