A generalization of the Landau-Lifschitz equation with uniaxial anisotropy is proposed, which can also reduce to the derivative nonlinear Schrödinger equation under an infinitesimal parameter. Based on the gauge transformation between Lax pairs, an N-fold generalized Darboux transformation is constructed for the generalization of the Landau-Lifschitz equation with uniaxial anisotropy. As applications of the N-fold generalized Darboux transformations, several types of exact solutions of the generalization of the Landau-Lifschitz equation with uniaxial anisotropy are obtained, including soliton solutions, Akhmediev breather solutions and rogue-wave solutions.

中文翻译：

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Landau-Lifschitz 方程的推广：呼吸和无赖波浪

提出了具有单轴各向异性的Landau-Lifschitz方程的推广，该方程还可以简化为无穷小参数下的导数非线性薛定谔方程。基于 Lax 对之间的规范变换，构造了 N 重广义 Darboux 变换，用于推广具有单轴各向异性的 Landau-Lifschitz 方程。作为N次广义Darboux变换的应用，得到了具有单轴各向异性的Landau-Lifschitz方程的推广的几种精确解，包括孤子解、Akhmediev呼吸器解和流氓波解。