An analytical consideration of a nonlocal nonlinear Schrödinger equation with distributed coefficients is presented. The analysis is twofold: first, exact solutions of the nonlocal equation with constant coefficients are found along with the appropriate conditions for their existence, and second, using a similarity transformation the distributed equation, i.e. the equations with varying coefficients, is reduced to the constant coefficients case; the solutions of the latter will be utilized in the construction of the solutions for the general case. This similarity transformation is also physically relevant as it allows for the physical parameters of the solution (amplitude, width, centre and phase) to vary in a specific way so that the constant coefficient system is a natural similarity reduction of the distributed case. Certain compatibility conditions needed for the consistency of this reduction are also deduced.

提出了具有分布系数的非局部非线性薛定ding方程的解析考虑。分析有两个方面：首先，找到具有常数系数的非局部方程的精确解以及存在它们的适当条件，其次，使用相似变换将分布方程（即具有变化系数的方程）简化为常数系数情况 后者的解决方案将用于构建一般情况的解决方案。这种相似性变换在物理上也很重要，因为它允许解决方案的物理参数（幅度，宽度，中心和相位）以特定方式变化，因此常数系数系统自然是分布式情况的相似性降低。