PreprintarXiv licencearXiv
Explicit meromorphic solutions of certain types of nonlinear differential-difference equations
Abstract
Our main purpose is to determine all meromorphic solutions, in explicit form, of the nonlinear differential-difference equations fn(z)f'(z)+q(z)f(z+c)=p1eα1z+p2eα2z and fn(z)f'(z)+q(z)eQ(z)f(z+c)=p1eα1z+p2eα2z, where n≥ 3 is an integer, q(z) and Q(z) are nonzero polynomials with Q(z) nonconstant, and c, pj, αj(j=1,2) are nonzero constants satisfying α1≠ α2. We sharpen the result in the cited literature, as illustrated by specific examples.
Related
- Meromorphic solutions of a nonlinear differential-difference equation with two exponential terms
- Existence and Nonexistence of Solutions of Certain type of Nonlinear Differential and Differential-Difference Equations
- Meromorphic solutions of first-order differential equations with rational exponential coefficients
- Stability and Periodicity Performance of Solutions of Nonlinear Difference Equations
- Entire solutions of Fermat-Type Partial Differential-Difference equations in higher dimensions
BibTeX
@misc{chen2026explicit,
title = {{Explicit meromorphic solutions of certain types of nonlinear differential-difference equations}},
author = {Minfeng Chen and Zongxuan Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30602},
eprint = {2610.30602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30602},
}
RIS
TY - UNPB
TI - Explicit meromorphic solutions of certain types of nonlinear differential-difference equations
AU - Minfeng Chen
AU - Zongxuan Chen
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30602
UR - https://arxiv.org/abs/2610.30602
AB - Our main purpose is to determine all meromorphic solutions, in explicit form, of the nonlinear differential-difference equations f^n(z)f'(z)+q(z)f(z+c)=p_1e^α_1z+p_2e^α_2z and f^n(z)f'(z)+q(z)e^Q(z)f(z+c)=p_1e^α_1z+p_2e^α_2z, where n≥ 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≠ α_2. We sharpen the result in the cited literature, as illustrated by specific examples.
ER -