AI 中文总结
本文研究一维对数修正非线性薛定谔方程，利用质量函数的解析性或单调性，证明了聚焦情形下有限个归一化驻波的存在及散焦情形下最小能量驻波的唯一性。
AI 中文摘要
在一维对数修正非线性薛定谔方程中，存在有限多个归一化驻波，这些驻波在空间平移和相位乘法下等价。在散焦情形下，对于给定的质量，存在唯一一个具有最小能量的归一化驻波。这两个结果均通过利用质量函数的性质获得：聚焦情形下的解析性，以及散焦情形下的单调性。
英文摘要
In the one-dimensional log-modified nonlinear Schrödinger equation, there are finitely many normalised standing-waves, up to space translation and phase multiplication. In the defocusing case, there is exactly one normalised standing-wave having a prescribed mass and least energy. Both results are obtained by exploiting properties of the mass function: the analyticity in the focusing case, and the monotonicity in the defocusing case.
Comments30 pages, 2 figures
