Lower bound for the lifespan of solutions to the generalized KdV equation with low-degree of nonlinearity

2020 ◽  
Author(s):  
Hayato Miyazaki
Keyword(s):  
Lower Bound ◽  
Kdv Equation ◽  
Generalized Kdv Equation ◽  
Low Degree

scholarly journals On a class of solutions to the generalized KdV type equation

2019 ◽  
Vol 21 (07) ◽  
pp. 1850056 ◽  
Author(s):  
Felipe Linares ◽  
Hayato Miyazaki ◽  
Gustavo Ponce
Keyword(s):  
Sobolev Space ◽  
Vries Equation ◽  
Weighted Sobolev Space ◽  
Kdv Equation ◽  
Local Existence ◽  
Type Equation ◽  
Well Posedness ◽  
Generalized Kdv Equation ◽  
Low Degree ◽  
Decay Of Solutions

We consider the IVP associated to the generalized KdV equation with low degree of nonlinearity [Formula: see text] By using an argument similar to that introduced by Cazenave and Naumkin [Local existence, global existence, and scattering for the nonlinear Schrödinger equation, Commun. Contemp. Math. 19(2) (2017) 1650038, MR3611666], we establish the local well-posedness for a class of data in an appropriate weighted Sobolev space. Also, we show that the solutions obtained satisfy the propagation of regularity principle proven in [P. Isaza, F. Linares and G. Ponce, On the propagation of regularity and decay of solutions to the [Formula: see text]-generalized Korteweg–de Vries equation, Comm. Partial Differential Equations 40(7) (2015) 1336–1364, MR3341207] in solutions of the [Formula: see text]-generalized KdV equation.

SOLVING THE GENERALIZED BURGERS–KdV EQUATION BY A COMBINATION METHOD

2008 ◽  
Vol 22 (21) ◽  
pp. 2021-2025 ◽  
Author(s):  
YUANXI XIE
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Combination Method ◽  
Generalized Kdv Equation ◽  
Generalized Burgers Equation

In view of the analysis on the characteristics of the generalized Burgers equation, generalized KdV equation and generalized Burgers–KdV equation, a combination method is presented to seek the explicit and exact solutions to the generalized Burgers–KdV equation by combining with those of the generalized Burgers equation and generalized KdV equation. As a result, many explicit and exact solutions for the generalized Burgers–KdV equation are successfully obtained by this technique.

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