On bi-Hamiltonian structure of two-component Novikov equation

2013 ◽  
Vol 377 (3-4) ◽  
pp. 257-261 ◽  
Author(s):  
Nianhua Li ◽  
Q.P. Liu
Keyword(s):  
Hamiltonian Structure ◽  
Two Component ◽  
Novikov Equation

scholarly journals On the Cauchy Problem for the Two-Component Novikov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu ◽  
Weian Tao
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Transport Equation ◽  
Besov Spaces ◽  
Well Posedness ◽  
Two Component ◽  
The Cauchy Problem ◽  
Novikov Equation

We are concerned with the Cauchy problem of two-component Novikov equation, which was proposed by Geng and Xue (2009). We establish the local well-posedness in a range of the Besov spaces by using Littlewood-Paley decomposition and transport equation theory which is motivated by that in Danchin's cerebrated paper (2001). Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time, which extend some results of Himonas (2003) to more general equations.

Integrable two-component systems of difference equations

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190668
Author(s):  
Pavlos Kassotakis ◽  
Maciej Nieszporski ◽  
Vassilios Papageorgiou ◽  
Anastasios Tongas
Keyword(s):  
Difference Equations ◽  
Discrete Version ◽  
Component Systems ◽  
Two Component ◽  
Two Component Systems ◽  
Novikov Equation

We present two lists of two-component systems of integrable difference equations defined on the edges of the Z 2 graph. The integrability of these systems is manifested by their Lax formulation which is a consequence of the multi-dimensional compatibility of these systems. Imposing constraints consistent with the systems of difference equations, we recover known integrable quad-equations including the discrete version of the Krichever–Novikov equation. The systems of difference equations give us in turn quadrirational Yang–Baxter maps.

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