scholarly journals Periodic wave solutions of a non-Newtonian filtration equation with an indefinite singularity

2021 ◽  
Vol 6 (2) ◽  
pp. 1209-1222
Author(s):  
Famei Zheng ◽  
Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2277-2292
Author(s):  
Weijun Xie ◽  
Fanchao Kong ◽  
Juan Nieto

This paper is concerned with a kind of non-Newtonian filtration equation with nonlinear sources and singularities. Based on the mountain pass theorem and variational methods, a sufficient criterion for the new results on the periodic wave solutions has been provided. Here not only the structure is more general and practical than the existing works but the conditions imposed are concise. Consequently, compared with the previous results on the singular equations and non-Newtonian filtration equations, the results we established are more generalized and some previous ones can been complemented and improved. Finally, the effectiveness of the established results are validated via two numerical examples and simulations.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mei Xu ◽  
Bo Du

AbstractA type of non-Newtonian filtration equations with variable delay is considered. Using a new approach which was established by Ge and Ren in (Nonlinear Anal. 58:477–488, 2004), we obtain the existence of periodic wave solutions for the non-Newtonian filtration equations. The methods of the present paper are markedly different from the existing ones.


2021 ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El–Barkouky ◽  
Hamdy Ahmed ◽  
Rabab M. I. El-Hassani ◽  
Ahmed H. Arnous

Abstract This paper studies Radhakrishnan-Kundu-Laksmannan equation which is used to describe the pulse propagation in optical fiber communications. By using improved modified extended tanh-function method various types of solutions are extracted such as bright solitons, singular solitons, singular periodic wave solutions, Jacobi elliptic solutions, periodic wave solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some of the obtained solutions are represented graphically.


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