We construct soliton solution of a variable coefficients nonlinear Schrödinger equation in the presence of parity reflection–time reversal \((\mathscr {PT})-\) symmetric Rosen–Morse potential using similarity transformation technique. We transform the variable coefficients nonlinear Schrödinger equation into the nonlinear Schrödinger equation with \(\mathscr {PT}-\)symmetric potential with certain integrability conditions. We investigate in-detail the features of the obtained soliton solutions with two different forms of dispersion parameters. Further, we analyze the nonlinear tunneling effect of soliton profiles by considering two different forms of nonlinear barrier/well and dispersion barrier/well. Our results show that the soliton can tunnel through nonlinear barrier/well and dispersion barrier/well with enlarged and suppressed amplitudes depending on the sign of the height. Our theoretical findings are experimentally realizable and might help to model the optical devices.

我们使用相似变换技术在存在奇偶反射-时间反转\((\mathscr {PT})-\)对称 Rosen-Morse 势的情况下构建可变系数非线性薛定谔方程的孤子解。我们用\(\mathscr {PT}-\)将变系数非线性薛定谔方程转化为非线性薛定谔方程具有一定可积性条件的对称势。我们详细研究了具有两种不同形式的色散参数的孤子解的特征。此外，我们通过考虑两种不同形式的非线性势垒/阱和色散势垒/阱来分析孤子剖面的非线性隧穿效应。我们的结果表明，孤子可以隧道穿过非线性势垒/井和色散势垒/井，其振幅根据高度的符号放大和抑制。我们的理论发现可以通过实验实现，并且可能有助于对光学设备进行建模。