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Phase Portraits of the Leslie-Gower System
In this paper we characterize the phase portraits of the Leslie-Gower model for competition among species. We give the complete description of their...
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Exact Solutions of a Nonlinear Diffusion Equation with Absorption and Production
We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model...
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Analysis of Solutions of Some Multi-Term Fractional Bessel Equations
We construct the existence theory for generalized fractional Bessel differential equations and find the solutions in the form of fractional or...
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Hyers—Ulam Stability of Second-Order Linear Dynamic Equations on Time Scales
We investigate the Hyers—Ulam stability (HUS) of certain second-order linear constant coefficient dynamic equations on time scales, building on...
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Nurowski’s Conformal Class of a Maximally Symmetric (2,3,5)-Distribution and its Ricci-flat Representatives
We show that the solutions to the second-order differential equation associated to the generalised Chazy equation with parameters k = 2 and k = 3...
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On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a0(x) + a1(x) y + a2(x) y2 + … + an(x) yn
In this paper we deal with differential equations of the form yy ′ = P ( x , y ) where y ′ = dy / dx and P ( x , y ) is a polynomial in the variables x and y of...
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On the Integrability of the Abel and of the Extended Liénard Equations
We present some exact integrability cases of the extended Liénard equation y ″ + f ( y )( y ′) n + k ( y )( y ′) m + g ( y ) y ′ + h ( y ) = 0, with n > 0 and m > 0...
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Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics
This article is devoted to the results of phase topology research on a generalized mathematical model, which covers such two problems as the dynamics...
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Linearization criteria for two-dimensional systems of third-order ordinary differential equations by complex approach
Linearization criteria for two-dimensional systems of second-order ordinary differential equations (ODEs) have been derived earlier using complex...
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On solutions of linear fractional differential equations and systems thereof
We derive exact solutions to classes of linear fractional differential equations and systems thereof expressed in terms of generalized Wright...
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The Group-Theoretical Analysis of Nonlinear Optimal Control Problems with Hamiltonian Formalism
In this study, we pay attention to novel explicit closed-form solutions of optimal control problems in economic growth models described by...
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On a surface isolated by Gambier
We provide a Lax pair for the surfaces of Voss and Guichard, and we show that such particular surfaces considered by Gambier are characterized by a...
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Liouvillian integrability of a general Rayleigh-Duffing oscillator
We give a complete description of the Darboux and Liouville integrability of a general Rayleigh-Duffing oscillator through the characterization of...
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GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems
Generalized Bäcklund–Darboux transformations (GBDTs) of discrete skew-selfadjoint Dirac systems have been successfully used for explicit solving of...
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Darboux polynomials, balances and Painlevé property
For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of...
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Bifurcation Analysis of the Dynamics of Two Vortices in a Bose–Einstein Condensate. The Case of Intensities of Opposite Signs
This paper is concerned with a system two point vortices in a Bose–Einstein condensate enclosed in a trap. The Hamiltonian form of equations of...
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Riccati equations and cone curves in Minkowski 3-space
In this paper, using the representation formula of cone curves and solving the Riccati equations respected to the structure function of cone curve,...