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arXiv · 2610.30602

Explicit meromorphic solutions of certain types of nonlinear differential-difference equations

Minfeng Chen·Zongxuan Chen
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Abstract

Our main purpose is to determine all meromorphic solutions, in explicit form, of the nonlinear differential-difference equations \begin{equation*} f^{n}(z)f'(z)+q(z)f(z+c)=p_{1}{\rm e}^{α_{1}z}+p_{2}{\rm e}^{α_{2}z} \end{equation*} and \begin{equation*} f^{n}(z)f'(z)+q(z){\rm e}^{Q(z)}f(z+c)=p_{1}{\rm e}^{α_{1}z}+p_{2}{\rm e}^{α_{2}z}, \end{equation*} where $n\geq 3$ is an integer, $q(z)$ and $Q(z)$ are nonzero polynomials with $Q(z)$ nonconstant, and $c,~p_{j},~α_{j}(j=1,2)$ are nonzero constants satisfying $α_{1}\neq α_{2}$. We sharpen the result in the cited literature, as illustrated by specific examples.

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Minfeng Chen, Zongxuan Chen. 2026-10-22. Explicit meromorphic solutions of certain types of nonlinear differential-difference equations. https://arxiv.org/abs/2610.30602

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