Local well‐posedness for a type of periodic fifth‐order Korteweg–de Vries equations without nonlinear dispersive term

2020 ◽  
Author(s):  
Deqin Zhou
Keyword(s):  
Well Posedness ◽  
De Vries ◽  
Fifth Order ◽  
Dispersive Term

scholarly journals Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
R. I. Nuruddeen ◽  
Khalid K. Ali ◽  
Lawal Muhammad ◽  
M. S. Osman ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Mathematical Physics ◽  
Order Derivative ◽  
Conformable Fractional Derivative ◽  
Fractional Order Derivative ◽  
De Vries ◽  
Fifth Order ◽  
2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

Global Well-Posedness for the Fifth-Order KdV Equation in $$H^{-1}(\pmb {\mathbb {R}})$$

Annals of PDE ◽  
2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Bjoern Bringmann ◽  
Rowan Killip ◽  
Monica Visan
Keyword(s):  
Kdv Equation ◽  
Well Posedness ◽  
Fifth Order
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