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In particular we consider the nonlinear partial differential equation $\\{ \\, \\rmi \\, \\partial_t + \\partial_x^2 + g |\\psi(x,t)|^2 - V^{+}(x) \\, \\} \\, \\psi(x,t) = 0$, where $V^{+}(x) = \\qty( -b^2 - m^2 + 1/4 ) \\, \\sech^2(x) - 2 i \\, m \\, b \\, \\sech(x) \\, \\tanh(x)$ represents the complex potential. Here we study the perturbation","authors_text":"Avadh Saxena, Avinash Khare, Bogdan Mihaila, Edward Arevalo, Franz G. Mertens, Fred Cooper, John F. Dawson, Niurka R. 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