Approximate Stationary Solitons of the Fifth Order Singularly Perturbed KdV-Type Equation

2001 ◽  
Vol 70 (9) ◽  
pp. 2525-2530
Author(s):  
Zuo-Nong Zhu Weimin Xue ◽  
Zuo-Min Zhu
Keyword(s):  
Type Equation ◽  
Singularly Perturbed ◽  
Fifth Order

scholarly journals Local Analyticity in the Time and Space Variables and the Smoothing Effect for the Fifth-Order KdV-Type Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-39
Author(s):  
Kyoko Tomoeda
Keyword(s):  
Kdv Equation ◽  
Type Equation ◽  
Smoothing Effect ◽  
Initial Value ◽  
Time And Space ◽  
Third Order ◽  
Bootstrap Argument ◽  
Real Analytic ◽  
Fifth Order ◽  
Bourgain Space

We consider the initial value problem for the reduced fifth-order KdV-type equation: , , , . This equation is obtained by removing the nonlinear term from the fifth-order KdV equation. We show the existence of the local solution which is real analytic in both time and space variables if the initial data satisfies the condition , for some constant . Moreover, the smoothing effect for this equation is obtained. The proof of our main result is based on the contraction principle and the bootstrap argument used in the third-order KdV equation (K. Kato and Ogawa 2000). The key of the proof is to obtain the estimate of on the Bourgain space, which is accomplished by improving Kenig et al.'s method used in (Kenig et al. 1996).

scholarly journals Low regularity for the fifth order Kadomtsev–Petviashvili-I type equation

2017 ◽  
Vol 263 (9) ◽  
pp. 5696-5726 ◽  
Author(s):  
Boling Guo ◽  
Zhaohui Huo ◽  
Shaomei Fang
Keyword(s):  
Type Equation ◽  
Low Regularity ◽  
Fifth Order

scholarly journals Nonexistence of Global Solutions to the Initial Boundary Value Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Changming Song ◽  
Jina Li ◽  
Ran Gao
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Type Equation ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Bond Number ◽  
Singularly Perturbed ◽  
Sixth Order ◽  
Initial Boundary Value

We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which describes the bidirectional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but very close to 1/3. The nonexistence of global solution to the initial boundary value problem for the singularly perturbed Boussinesq-type equation is discussed and two examples are given.

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