Isolated periodic wave solutions arising from Hopf and Poincaré bifurcations in a class of single species model

2022 ◽  
Vol 311 ◽  
pp. 59-80
Author(s):  
Qinlong Wang ◽  
Yu'e Xiong ◽  
Wentao Huang ◽  
Pei Yu
Keyword(s):  
Single Species ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Single Species Model

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.

scholarly journals Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Ming Song ◽  
Zhengrong Liu
Keyword(s):  
Dynamical Systems ◽  
Solitary Wave ◽  
Blow Up ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Bbm Equation

We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.

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