scholarly journals Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Siqi Chen ◽  
Yong-Kui Chang ◽  
Yanyan Wei
Keyword(s):  
Evolution Equation ◽  
Periodic Solutions

scholarly journals Exact Periodic Solutions of the Nonintegrable Kawahara Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Ognyan Yordanov Kamenov ◽  
Anna P. Angova
Keyword(s):  
Evolution Equation ◽  
Periodic Solutions ◽  
Transformation Method ◽  
Periodic Waves ◽  
Kawahara Equation ◽  
Bilinear Transformation ◽  
The Real ◽  
Single Solution ◽  
Spatial Displacements ◽  
Phase Solution

In the present paper, we have obtained an exact biperiodic, one-phase solution of the Kawahara evolution equation. Two classes of real periodic waves generated by the biperiodic solution have been analyzed. A modification of the bilinear-transformation method has been applied allowing to provide a single solution of the residual equation derived from the bidifferential reduction of the considered nonintegrable equation. It is shown that the spatial displacements are individual for each separate harmonic of the real periodic solutions.

scholarly journals Existence and Global Asymptotic Behavior of S -Asymptotically ω -Periodic Solutions for Evolution Equation with Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hong Qiao ◽  
Qiang Li ◽  
Tianjiao Yuan
Keyword(s):  
Asymptotic Behavior ◽  
Evolution Equation ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Compact Semigroup ◽  
Existence Results ◽  
Asymptotically Periodic ◽  
Abstract Evolution Equation ◽  
Equation With Delay ◽  
Asymptotically Periodic Solutions

This paper is concerned with the abstract evolution equation with delay. Firstly, we establish some sufficient conditions to ensure the existence results for the S -asymptotically periodic solutions by means of the compact semigroup. Secondly, we consider the global asymptotic behavior of the delayed evolution equation by using the Gronwall-Bellman integral inequality involving delay. These results improve and generalize the recent conclusions on this topic. Finally, we give an example to exhibit the practicability of our abstract results.

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