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Research articles

ScienceAsia 49 (2023):ID 108-115 |doi: 10.2306/scienceasia1513-1874.2023.133


Meromorphic solutions of the seventh-order KdV equation by using an extended complex method and Painlevé analysis


Guoqiang Dang

 
ABSTRACT:     Using the traveling wave transformation, the seventh-order KdV equation reduces to a sixth-order complex differential equation (CDE), and we first prove that all meromorphic solutions of the CDE belong to the class W via Nevanlinna?s value distribution theory. Then abundant new meromorphic solutions of the sixth-order CDE have been established in the finite complex plane with the aid of an extended complex method and Painlev? analysis, which contains Weierstrass elliptic function solutions and exponential function solutions, some of them are whole new solutions comparing to the opening literature. We give the computer simulations of some elliptic and exponential solutions. At last, we investigate the meromorphic solutions of the nonlinear dispersive Kawahara equation as an application.

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a School of Mathematical Sciences, Beijing Normal University, Beijing 10085 China

* Corresponding author, E-mail: dang@mail.bnu.edu.cn

Received 3 Nov 2020, Accepted 17 Aug 2022