具有光滑 $L^2$-次临界函数非线性扰动的对数 Schrödinger 方程多孤子的存在性
Existence of multi-solitons for logarithmic Schr{ö}dinger equation with a perturbation of a smooth $L^2$-subcritical function nonlinearity
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中文总结 AI 辅助
本文针对含聚焦对数项和光滑 $L^2$-次临界函数非线性的 Schrödinger 方程，通过迭代构造与局部能量估计，证明了多孤子解的存在性，其渐近表现为多个不同速度孤子的叠加。
中文摘要 AI 辅助
本文研究具有聚焦对数项和光滑 $L^2$-次临界函数组合的非线性 Schrödinger 方程。我们的主要结果是构造该方程的多孤子解。这些特殊构型在长时间渐近行为上表现为多个以不同速度运动的孤子的叠加。证明依赖于迭代构造方法，并结合适用于非线性混合结构的局部能量估计。
英文摘要
In this paper, we study the nonlinear Schr{ö}dinger equation with a nonlinearity combining a focusing logarithmic term and a smooth $L^2$-subcritical function. Our main result is the construction of multisoliton solutions for this equation. These special configurations behave asymptotically, for large times, as the superposition of several solitons moving with distinct velocities. The proof relies on an iterative construction method combined with localized energy estimates adapted to the mixed structure of the nonlinearity.
