Higher-order smooth profiles and breather-positon phenomena in the Kuralay equation
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.
In this study, we investigate the fractional telegraph equation, a key nonlinear model for signal transmission, wave propagation, and complex dynamical systems in engineering.
A key research challenge in modern cryptography is the construction of robust nonlinear components that simultaneously achieve high nonlinearity, resistance to linear and differential…
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…