scholarly journals A uniqueness theorem for the two-dimensional generalized Korteweg-de Vries equation

1991 ◽  
Vol 158 (1) ◽  
pp. 203-212 ◽  
Author(s):  
Daxin Wu ◽  
Shih-liang Wen
Keyword(s):  
Uniqueness Theorem ◽  
Vries Equation ◽  
Two Dimensional ◽  
De Vries

On the two - dimensional nonlinear Korteweg - de Vries equation with cubic stream function

2016 ◽  
Vol 10 ◽  
pp. 157-165 ◽  
Author(s):  
Sergei Evgenievich Ivanov ◽  
Vitaly Gennadievich Melnikov
Keyword(s):  
Stream Function ◽  
Vries Equation ◽  
Two Dimensional ◽  
De Vries

Interpretation of three-soliton interactions in terms of resonant triads

1978 ◽  
Vol 87 (1) ◽  
pp. 17-31 ◽  
Author(s):  
D. Anker ◽  
N. C. Freeman
Keyword(s):  
Soliton Solution ◽  
Analytic Solution ◽  
Vries Equation ◽  
Two Dimensional ◽  
Soliton Interactions ◽  
Resonant Interactions ◽  
De Vries ◽  
Computer Calculations ◽  
Resonant Triads

The three-soliton solution of the two-dimensional Korteweg-de Vries equation is analysed to show that the structure of the interaction can be represented in terms of the motion of two-soliton resonant interactions (resonant triads) as described by Miles (1977). The schematic development of the interaction with time is obtained and shown to approximate closely to computer calculations of the analytic solution. Similar results follow for interactions of more solitons and other equations.

CARLEMAN ESTIMATE AND UNIQUE CONTINUATION PROPERTY FOR THE LINEAR STOCHASTIC KORTEWEG–DE VRIES EQUATION

2014 ◽  
Vol 90 (2) ◽  
pp. 283-294 ◽  
Author(s):  
PENG GAO
Keyword(s):  
Galerkin Method ◽  
Uniqueness Theorem ◽  
Vries Equation ◽  
Unique Continuation ◽  
Carleman Estimate ◽  
Well Posedness ◽  
Unique Continuation Property ◽  
De Vries ◽  
Continuation Property ◽  
The Galerkin Method

AbstractIn this paper, we obtain the well posedness of the linear stochastic Korteweg–de Vries equation by the Galerkin method, and then establish the Carleman estimate, leading to the unique continuation property (UCP) for the linear stochastic Korteweg–de Vries equation. This UCP cannot be obtained from the classical Holmgren uniqueness theorem.

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