scholarly journals New approaches for periodic wave solutions of a non-Newtonian filtration equation with variable delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mei Xu ◽  
Bo Du
Keyword(s):  
Periodic Wave ◽  
Variable Delay ◽  
New Approach ◽  
Filtration Equation ◽  
Periodic Wave Solutions ◽  
New Approaches ◽  
Nonlinear Anal ◽  
Wave Solutions

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.

scholarly journals Periodic wave solutions of non-Newtonian filtration equations with nonlinear sources and singularities

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2277-2292
Author(s):  
Weijun Xie ◽  
Fanchao Kong ◽  
Juan Nieto
Keyword(s):  
Variational Methods ◽  
Mountain Pass Theorem ◽  
Periodic Wave ◽  
Mountain Pass ◽  
Sufficient Criterion ◽  
Filtration Equation ◽  
Numerical Examples ◽  
Periodic Wave Solutions ◽  
Singular Equations ◽  
Wave Solutions

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.

scholarly journals Optical solutions and other solutions for Radhakrishnan-Kundu-Laksmannan equation by using improved modified extended tanh-function method

2021 ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El–Barkouky ◽  
Hamdy Ahmed ◽  
Rabab M. I. El-Hassani ◽  
Ahmed H. Arnous
Keyword(s):  
Optical Fiber ◽  
Function Method ◽  
Pulse Propagation ◽  
Periodic Wave ◽  
Optical Fiber Communications ◽  
Periodic Wave Solutions ◽  
Bright Solitons ◽  
Wave Solutions ◽  
Elliptic Solutions ◽  
Fiber Communications

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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