In this paper, an extended (3+1)-dimensional nonlinear Schrödinger equation is studied. By using similarity transformation, some exact solutions of this equation are obtained, which include soliton solutions and periodic function solutions, its nonlinear spatial modulation and external potential are affected by time and space. Based on the solution obtained previously, some figures are displayed.

中文翻译：

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时空变化系数的(3+1)维非线性薛定谔方程的相似变换和精确解


本文研究了扩展的(3+1)维非线性薛定谔方程。利用相似变换，得到了该方程的一些精确解，包括孤子解和周期函数解，其非线性空间调制和外势受时间和空间的影响。根据之前获得的解决方案，显示一些数字。