AI 中文总结
该研究采用带谱扰动的广义长波极限方法，得到 mKP-I 方程的二阶、三阶新型 lump 解，发现其与 KP-I 方程的相互作用动力学存在差异，为相关方程的解研究提供了新结果。
AI 中文摘要
我们通过应用带有谱扰动的广义长波极限方法，构造了修正的Kadomtsev-Petviashvili-I（mKP-I）方程的新型高阶 lump 解。通过调整孤子解中的相位参数，我们得到了二阶和三阶 lump 解，据我们所知，这些是 mKP-I 方程的相关首次报道。详细的渐近分析表明，这些简并 lump 表现出与 KP-I 方程中类似的反常散射。然而，与 KP-I 情况不同，碰撞后不会出现完全的能量均分，且两个 lump 在其渐近振幅的次阶项中仍保持可区分性。这一区别凸显了修正型与标准型 KP-I 方程之间相互作用动力学的差异。
英文摘要
We construct novel higher-order lump solutions of the modified Kadomtsev-Petviashvili-I (mKP-I) equation by applying the generalized long-wave limit method with spectral perturbations. By tuning the phase parameters in the soliton solution, we obtain second- and third-order lump solutions, which, to the best of our knowledge, are reported here for the first time for the mKP-I equation. A detailed asymptotic analysis reveals that these degenerate lumps exhibit anomalous scattering analogous to that in the KP-I equation. However, in contrast to the KP-I case, no complete energy equipartition occurs after the collision, and the two lumps remain distinguishable in the subleading terms of their asymptotic amplitudes. This distinction highlights a difference in the interaction dynamics between the modified and standard KP-I equations.
