Advances in International Applied Mathematics
Advances in International Applied Mathematics. 2025; 7: (1) ; 10.12208/j.aam.20250001 .
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扬州大学数学科学学院 江苏扬州
*通讯作者： 顾佳鑫,单位：扬州大学数学科学学院 江苏扬州；
高阶Heisenberg方程作为非线性科学和数学物理领域的重要模型，其解的结构和动力学行为一直是研究热点。本研究基于贝克隆变换理论，构建了高阶Heisenberg方程的贝克隆变换，并将其作用于平凡解而成功生成了呼吸子解和孤子解。通过详细分析，揭示了这些解在单位球面上的轨迹曲线具有自交点序列且收敛于北极点的特性。研究结果为深入理解高阶Heisenberg方程的解结构和动力学行为提供了新视角，对非线性科学和数学物理领域的相关研究具有重要参考价值。
The higher-order Heisenberg equation is a significant model in the fields of nonlinear science and mathematical physics. The study of its solution structures and dynamical behaviors has always been a hot research area. In this paper, we first construct Bäcklund transformation for the higher-order Heisenberg equation, and then by applying it to a trivial solution, we successfully generate breather and soliton solutions. Through detailed analysis, we reveal that the trajectory curve of these solutions on the unit sphere exhibits a sequence of self-intersection points, which finally converges toward the north pole. The results of this paper provide a new insight into its solution structures and dynamical behaviors, and hold significant reference value for related research in nonlinear science and mathematical physics.
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