@article{Alammari2026, 
author = {Maha Alammari and Muhammad Yasir and Solomon Manukure},
title = {Higher-order smooth profiles and breather-positon phenomena in the Kuralay equation},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {11580-11594},
keywords = {degenerate Darboux transformation, Positon solutions, phase Shifts, breather-positon},
url = {https://www.sciopen.com/article/10.3934/math.2026477},
doi = {10.3934/math.2026477},
abstract = {In this paper, we investigated higher-order smooth positon and breather-positon solutions of the Kuralay equation. Starting from the associated Lax pair, we constructed an explicit    N-fold Darboux transformation (DT) in determinant form. By introducing a spectral parameter degeneration procedure combined with higher-order Taylor expansion, we derived smooth higher-order positon solutions from multi-soliton solutions. Furthermore, under nonvanishing boundary conditions, breather-positon solutions were obtained. The dynamical properties of these solutions were analyzed, revealing elastic interaction behavior and nontrivial phase shifts. The results provided a unified framework for constructing degenerate localized wave structures and extended existing studies on the Kuralay equation.}
}