Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order for describing nonlinear waves in gas-liquid mixtures are derived. Exact solutions of these nonlinear evolution equations are found. Properties of nonlinear waves in a liquid with gas bubbles are discussed.

Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational, periodic, elliptic) are found for a wide class of autonomous nonlinear ordinary differential equations.

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Rational solutions and special polynomials associated with the generalized K 2 hierarchy are studied. This hierarchy is related to the Sawada -Kotera and Kaup -Kupershmidt equations and some other integrable partial differential equations including the Fordy -Gibbons equation. Differential -difference relations and differential equations satisfied by the polynomials are derived. The relationship between these special polynomials and stationary configurations of point vortices with circulations Γ and −2Γ is established. Properties of the polynomials are studied. Differential -difference relations enabling one to construct these polynomials explicitly are derived. Algebraic relations satisfied by the roots of the polynomials are found.