# Bifurcation of Soliton Families from Linear Modes in Non‐PT‐Symmetric Complex Potentials

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Continuous families of solitons in the nonlinear Schrödinger equation with non‐$\mathcal{PT}$‐symmetric complex potentials and general forms of nonlinearity are studied analytically. Under a weak assumption, it is shown that stationary equations for solitons admit a constant of motion if and only if the complex potential is of a special form ${g}^{2}\left(x\right)+i{g}^{\prime }\left(x\right)$, where $g\left(x\right)$ is an arbitrary real function. Using this constant of motion, the second‐order complex soliton equation is reduced to a new second‐order real equation for the amplitude of the soliton. From this real soliton equation, a novel perturbation technique is employed to show that continuous families of solitons bifurcate out from linear discrete modes in these non‐$\mathcal{PT}$‐symmetric complex potentials. All analytical results are corroborated by numerical examples.
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Document Type: Research Article

Publication date: May 1, 2016

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