scholarly journals Embedded exponential-type low-regularity integrators for KdV equation under rough data

2021 ◽  
Author(s):  
Yifei Wu ◽  
Xiaofei Zhao
Keyword(s):  
Exponential Type ◽  
Kdv Equation ◽  
Low Regularity

Low regularity Cauchy problem for the fifth-order modified KdV equations on 𝕋

2018 ◽  
Vol 15 (03) ◽  
pp. 463-557 ◽  
Author(s):  
Chulkwang Kwak
Keyword(s):  
Kdv Equation ◽  
Main Tool ◽  
Well Posedness ◽  
Current Form ◽  
Low Regularity ◽  
Integrable Structure ◽  
Fourier Restriction ◽  
Fourier Restriction Norm Method ◽  
Modified Kdv Equation ◽  
Fifth Order

We consider the fifth-order modified Korteweg–de Vries (modified KdV) equation under the periodic boundary condition. We prove the local well-posedness in [Formula: see text], [Formula: see text], via the energy method. The main tool is the short-time Fourier restriction norm method, which was first introduced in its current form by Ionescu, Kenig and Tataru [Global well-posedness of the KP-I initial-value problem in the energy space, Invent. Math. 173(2) (2008) 265–304]. Besides, we use the frequency localized modified energy to control the high-low interaction component in the energy estimate. We remark that under the periodic setting, the integrable structure is very useful (but not necessary) to remove harmful terms in the nonlinearity and this work is the first low regularity well-posedness result for the fifth-order modified KdV equation.

scholarly journals Low regularity stability of solitons for the KDV equation

2003 ◽  
Vol 2 (3) ◽  
pp. 277-296 ◽  
Author(s):  
S. Raynor ◽  
◽  
G. Staffilani
Keyword(s):  
Kdv Equation ◽  
Low Regularity ◽  
The Kdv Equation

scholarly journals An exponential-type integrator for the KdV equation

2016 ◽  
Vol 136 (4) ◽  
pp. 1117-1137 ◽  
Author(s):  
Martina Hofmanová ◽  
Katharina Schratz
Keyword(s):  
Exponential Type ◽  
Kdv Equation ◽  
The Kdv Equation

scholarly journals The low regularity global solutions for the critical generalized KdV equation

2010 ◽  
Vol 7 (3) ◽  
pp. 265-288 ◽  
Author(s):  
Changxing Miao ◽  
Shuanglin Shao ◽  
Yifei Wu ◽  
Guixiang Xu
Keyword(s):  
Kdv Equation ◽  
Global Solutions ◽  
Low Regularity ◽  
Generalized Kdv Equation
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