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Quantum Sturm–Liouville problems introduced in our paper (Büyükaşık et al. in J Math Phys 50:072102, 2009) provide a reach set of exactly solvable quantum damped parametric oscillator models. Based on these results, in the present paper we study a set of variable parametric nonlinear Madelung fluid models and corresponding complex Burgers equations, related to the classical orthogonal polynomials...
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