Higher-order smooth profiles and breather-positon phenomena in the Kuralay equation

Maha Alammari; Muhammad Yasir; Solomon Manukure; Maha Alammari; Muhammad Yasir; Solomon Manukure

doi:10.3934/math.2026477

AIMS Mathematics

2026, Volume 11, Issue 4: 11580-11594. doi: 10.3934/math.2026477

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Higher-order smooth profiles and breather-positon phenomena in the Kuralay equation

1.
Department of Mathematics, College of Science, King Saud University, P.O. Box 22452 Riyadh 11495, Saudi Arabia
2.
School of Mathematics, Hefei University of Technology, Hefei 230009, China
3.
Florida A & M University, Tallahassee, FL, 3230, USA

Received: 20 February 2026 Revised: 13 April 2026 Accepted: 21 April 2026 Published: 27 April 2026
MSC : 35J05, 35K05, 35L05, 37K40

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.
- degenerate Darboux transformation,
- Positon solutions,
- phase Shifts,
- breather-positon
Citation: Maha Alammari, Muhammad Yasir, Solomon Manukure. Higher-order smooth profiles and breather-positon phenomena in the Kuralay equation[J]. AIMS Mathematics, 2026, 11(4): 11580-11594. doi: 10.3934/math.2026477

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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.

References

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