Buyukasik, Sirin A.Pashaev, Oktay K.2024-08-202024-08-20201240259-97911572-889710.1007/s10910-012-0060-4https://doi.org/10.1007/s10910-012-0060-4https://premium.gcris.co/handle/123456789/72Pashaev, Oktay/0000-0002-6249-1277; Atilgan Buyukasik, Sirin/0000-0001-7731-070XQuantum Sturm-Liouville problems introduced in our paper (BuyukaAYA +/- k 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 of Hermite, Laguerre and Jacobi types. We show that the nonlinear systems admit direct linearazation in the form of Schrodinger equation for a parametric harmonic oscillator, allowing us to solve exactly the initial value problems for these equations by the linear quantum Sturm-Liouville problem. For each type of equations, dynamics of the probability density and corresponding zeros, as well as the complex velocity field and related pole singularities are studied in details.eninfo:eu-repo/semantics/openAccessSchroedinger equationDamped parametric harmonic oscillatorSturm-Liouville problemsQuantum hydrodynamicsMadelung fluidBurgers equationPole dynamicsTime variable parametersExact solvabilitytext::journal::journal article