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Meromorphic solutions of nonlinear ordinary differential equations
Nikolay A. Kudryashov
Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear…
Exact solutions of equations for the Burgers hierarchy
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
Some classes of the rational, periodic and solitary wave solutions for the Burgers hierarchy are presented. The solutions for this hierarchy are obtained by using the generalized C…
Self-similar solutions of the Burgers hierarchy
Nikolai A. Kudryashov
Self-similar solutions of the equations for the Burgers hierarchy are presented.
Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation
Nikolai A. Kudryashov
The generalized Kuramoto-Sivashinsky equation in the case of the power nonlinearity with arbitrary degree is considered. New exact solutions of this equation are presented.
Nonlinear evolution equations for describing waves in bubbly liquids with viscosity and heat transfer consideration
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscos…
Exact solutions of the Swift-Hohenberg equation with dispersion
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
The Swift-Hohenberg equation with dispersion is considered. Traveling wave solutions of the Swift-Hohenberg equation with dispersion are presented. The classification of these solu…
Meromorphic exact solutions of the generalized Bretherton equation
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, Maria V. Demina
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the g…
Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
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. Nonli…
On elliptic solutions of nonlinear ordinary differential equations
Maria V. Demina, Nikolay A. Kudryashov
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the g…
Point vortices and polynomials of the Sawada-Kotera and Kaup-Kupershmidt equations
Maria V. Demina, Nikolay A. Kudryashov
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…
Vortices ans Polynomials: Nonuniqueness of the Adler-Moser polynomials for the Tkachenko equation
Maria V. Demina, Nikolay A. Kudryashov
Stationary and translating relative equilibria of point vortices in the plane are studied. It is shown that stationary equilibria of a system containing point vortices with arbitra…