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Research articles

ScienceAsia 50 (2024):ID 2024032 1-9 |doi: 10.2306/scienceasia1513-1874.2024.032


The study of solutions of several systems of the product type nonlinear partial differential difference equations


Yi Hui Xua, Xiao Lan Liua, Hong Yan Xua,b,*, Nan Lic

 
ABSTRACT:      The purpose of this article is to investigate the solutions of several systems of the nonlinear partial differential difference equations (PDDEs) (including second order partial differential, mixed partial differential and complex difference)  f (z + c)(gz1 + gz1z1 ) = 1, g(z + c)(f z1 + f z1z1 ) = 1,  f (z + c)(gz1 + gz1z2 ) = 1, g(z + c)(f z1 + f z1z2 ) = 1, and  f (z + c)(f z1 + gz1z2 ) = 1, g(z + c)(gz1 + f z1z2 ) = 1, where c = (c1 ,c2 ) ? C 2 . We establish some theorems concerning the forms of the pair of solutions for these systems of PDDEs which are some improvements and generalization of the previous results given by Gao, Liu and Xu. Moreover, some examples show that the forms of solutions of our theorems are precise to some extent.

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a School of Arts and Sciences, Suqian University, Suqian, Jiangsu 223800 China
b School of Mathematics and Computer Science, Shangrao Normal University, Shangrao Jiangxi 334001 China
c School of Mathematics, Qilu Normal University, Jinan, Shandong 250200 China

* Corresponding author, E-mail: xhyhhh@126.com

Received 31 Aug 2023, Accepted 21 Dec 2023