Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations

получена 12 августа 2014Ключевые слова: мероморфные решения, эллиптические решения, автономные нелинейные дифференциальные уравненияРассматривается задача построения и классификации эллиптических ре-шений нелинейных дифференциальных уравнений. Описывается эффектив-ный метод, позволяющий находить любое эллиптическое решение автономного нелинейного обыкновенного дифференциального уравнения. Метод не требу-ет интегрирования дополнительных дифференциальных уравнений. Большое внимание уделяется методике построения эллиптических решений с нескольки-ми полюсами в параллелограмме периодов. С помощью данного метода найден явный вид всех эллиптических решений до четвертого порядка включитель-но для обыкновенного дифференциального уравнения, имеющего ряд физиче-ских приложений. Рассматриваемый метод допускает естественное обобщение на случай систем обыкновенных дифференциальных уравнений.

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Section: эллиптические решения обыкновенных дифференциальных уравненийunclassified

Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations

Кудряшов¹,

Демина²

2014

Model. anal. inf. sist.

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“…This equation is called a balance equation [13,14]. We note that the method of the simplest equation and its modified version are closely connected to the problem for obtaining meromorphic solutions of nonlinear partial differential equations [15,16]. By the methodology described in [15,16] one can obtain other interesting classes of solutions of nonlinear PDEs such as rational solutions for example.…”

Section: The Methods Of the Simplest Equationmentioning

confidence: 99%

“…We note that the method of the simplest equation and its modified version are closely connected to the problem for obtaining meromorphic solutions of nonlinear partial differential equations [15,16]. By the methodology described in [15,16] one can obtain other interesting classes of solutions of nonlinear PDEs such as rational solutions for example. In addition we stress that by means of the traveling wave ansatz one reduces the nonlinear PDE to a nonlinear ODE and after this if an appropriate simplest ODE exists then a particular solution can be obtained that usually depends on as many parameters of the problem as possible.…”

Section: The Methods Of the Simplest Equationmentioning

confidence: 99%

On Nonlinear Dynamics of the STAT5a Signaling Protein

Nikolova

Jordanov

Vitanov

2014

BIOMATH

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Abstract-In this paper we model dynamics of cross talk between MEK/ERK and JAK/STAT signaling pathways by means of nonlinear ordinary differential equations. The considered system of four ordinary differential equations is reduced to one ordinary differential equation, representing dynamics of the phosphorylated STAT5a signaling protein. We show that the diffusion together with the corresponding biochemical reactions is likely to play a critical role in governing the dynamical behavior of the considered signaling protein. By the modified method of simplest equation to the described reaction-diffusion equation we obtain an analytical solution which explains drop and jump propagation of the STAT5a protein concentration.

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“…The second method [11,12] implements another classical result of Hermite [15], stating that any elliptic or degenerate elliptic function admits a unique decomposition in simple elements…”

Section: Second Methodsmentioning

confidence: 99%