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 Foreword 3 On the relation between the continuous and discrete Painlevé equationsP. A. Clarkson, E. L. Mansfield, H. N. Webster 5 An elementary approach to the polynomial $\tau$-functions of the KP hierarchyG. Falqui, F. Magri, M. Pedroni, J. P. Zubelli 23 A new construction of recursion operators for systems of the hydrodynamic typeA. P. Fordy, T. B. Gürel 37 An analogue of the Moutard transformation for the Goursat equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$E. I. Ganzha 50 Existence of a global solution of the Whitham equationsT. Grava 58 Nonlinear fourth-order differential equations with solutions in the form of transcendentsN. A. Kudryashov 72 Integrable ordinary differential equations on free associative algebrasA. V. Mikhailov, V. V. Sokolov 88 Bäcklund transformations for hyperbolic surfaces in $E^3$ via Weingarten congruencesM. Nieszporski, A. Sym 102 Asymptotic approximations for a new eigenvalue in linear problems without a thresholdD. E. Pelinovsky, C. Sulem 118 Initial boundary value problems for the nonlinear Schrödinger equationB. Pelloni 128 Factoring linear partial differential operators and the Darboux method for integrating nonlinear partial differential equationsS. P. Tsarev 144