Results 221 to 230 of about 101,253 (259)

On Meromorphic Solutions of Nonlinear Complex Differential Equations

Analysis Mathematica, 2023
The paper describes the meromorphic solutions of differential equations of a special form. Its main result is the following theorem:\par Theorem. Let \(n\ge 3\), \(d\ge 0\) and \(m\ge 1\) be integers, \(n\ge m\) and \(P(z,f,f^{'},\dots,f^{(d)})\) be a differential polynomial in \(f(z)\) of degree \(d\le n\) with small functions of \(f(z)\) as its ...
Chen, J.-F., Feng, Y.-Y.
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Complex Second-Order Differential Equations and Separability

Applicable Algebra in Engineering, Communication and Computing, 2001
\textit{E.~Martinez, J.~Carinena}, and \textit{W.~Sarlet} [Math. Proc. Camb. Philos. Soc. 113, No.1, 205-224 (1993; Zbl 0803.34010)] provided the necessary and sufficient conditions for a system of \(n\) second order ordinary differential equations on a manifold \(M\) to decompose into \(n\) independent 1-dimensional second order differential equations.
W. Sarlet, G. Thompson
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Integration of Complex Differential Equations

Journal of Dynamical and Control Systems, 1999
The problem of integration of complex differential equations is considered from several viewpoints: Liouvillian integration, the study of the holonomy groups associated with compact leaves of the holomorphic foliation subjacent to the differential equation and construction of the transverse structure of the foliation.
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Complex Partial Differential Equations

Journal of Mathematical Sciences
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aksoy, Ü., Begehr, H., Çelebi, A., Shupeyeva, B.   +3 more
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The complexity of stochastic differential equations

Stochastics, 1981
There has been considerable interest lately in the complexity of solving stochastic differential equations, for example, can they be solved individually for each sample path. In this note we unify what several researchers have indicated, namely that the stochastic complexity depends on the Lie algebra generated by the vector fields multiplying the ...
Arthur J. Krener, Claude Lobry
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On meromorphic complex differential equations

Dynamics and Stability of Systems, 1994
In this paper, we study first-order, autonomous, complex differential equations of the form i = f (z), where f (z) is the meromorphic function of the complex variable z, defined in a simply connected domain on the Riemann sphere. We concentrate on the phase portraits of such systems, with particular attention being paid to the existence and properties ...
D. J. Needham, A.C. King
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Complex Solutions of Partial Differential Equations

American Journal of Mathematics, 1946
Not ...
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Partial differential equation diffusion in complex domain

2016 International Conference on Advances in Computing, Communications and Informatics (ICACCI), 2016
In the course of noise removal by means of anisotropic diffusion method, it is important to maintain image smooth and preserve image features. In this paper, a new anisotropic diffusion in complex field is proposed with better smoothing effects as well as well preverving image edges well. Experiment results have shown the effectiveness of this proposed
Lanlan Li, Jinsong Wu 0001
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Complex ΨDOSS and systems of complex differential equations

2015
In Chapters 4–7 we discussed pseudo-differential equations of integer and fractional orders with ψDOSS depending on real variables \(t \in \mathbb{R}\) and \(x \in \mathbb{R}^{n}\). In this section we will discuss differential and pseudo-differential equations depending on complex variables \(t =\tau +i\sigma \in \mathbb{C}\) and \(z = x + iy \in ...
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Solving Differential Equations Without Complex Numbers

Mathematics Magazine, 1957
The only place in a course in real differential equations that complex numbers arise (embarrassingly, I'm afraid) is in the study of the linear equation with constant coefficients. This seems to imply that the theory is not complete in itself, without trespassing into -the complex number field.
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