Results 1 to 10 of about 290,052 (170)
Polynomial Solutions of Equivariant Polynomial Abel Differential Equations [PDF]
Advanced Nonlinear Studies, 2018 Let a(x){a(x)} be non-constant and let bj(x){b_{j}(x)}, for j=0,1,2,3{j=0,1,2,3}, be real or complex polynomials in the variable x. Then the real or complex equivariant polynomial Abel differential equation a(x)y˙=b1(x)y+b3(x)y3{a(x)\dot{y}=b_{1}(
Llibre Jaume, Valls Clàudia
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Exponential Polynomials and Nonlinear Differential-Difference Equations [PDF]
Journal of Function Spaces, 2020 In this paper, we study finite-order entire solutions of nonlinear differential-difference equations and solve a conjecture proposed by Chen, Gao, and Zhang when the solution is an exponential polynomial.
Junfeng Xu, Jianxun Rong
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Journal of High Energy Physics, 2018 The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations.
R. S. Vieira
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Conditions for asymptotic stability of first order scalar differential-difference equation with complex coefficients [PDF]
Archives of Control Sciences, 2023 We investigate a scalar characteristic exponential polynomial with complex coefficients associated with a first order scalar differential-difference equation.
Rafał Kapica, Radosław Zawiski
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Mathematics, 2021 Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green’s function, in the ...
Tohru Morita, Ken-ichi Sato
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New optical soliton solutions to the (n+1) dimensional time fractional order Sinh-Gordon equation
Results in Physics, 2023 This article studies and constructs new optical soliton solutions for the (n+1)-dimensional time fractional order Sinh-Gordon equation. First, we change the differential equation into Ordinary differential equation which is connected with a quartic ...
Da Shi, Zhao Li
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Interpretable polynomial neural ordinary differential equations
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023 Neural networks have the ability to serve as universal function approximators, but they are not interpretable and do not generalize well outside of their training region. Both of these issues are problematic when trying to apply standard neural ordinary differential equations (ODEs) to dynamical systems. We introduce the polynomial neural ODE, which is
Colby Fronk, Linda Petzold
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Differential Equations for Jacobi-Pineiro Polynomials [PDF]
Computational Methods and Function Theory, 2006 For $r\in \Z_{\geq 0}$, we present a linear differential operator %$(\di)^{r+1}+ a_1(x)(\di)^{r}+...+a_{r+1}(x)$ of order $r+1$ with rational coefficients and depending on parameters. This operator annihilates the $r$-multiple Jacobi-Pi eiro polynomial.
Mukhin, Eugene, Varchenko, Alexander
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Gradient Structures Associated with a Polynomial Differential Equation
Mathematics, 2020 In this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in R n is described by solving the Cauchy Problem for the corresponding first order system of PDEs.
Savin Treanţă
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Simple Equations Method and Non-Linear Differential Equations with Non-Polynomial Non-Linearity
Entropy, 2021 We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an appropriate
Nikolay K. Vitanov +1 more
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