scholarly journals Integrable discretization and deformation of the nonholonomic Chaplygin ball

2017 ◽  
Vol 22 (4) ◽  
pp. 353-367 ◽  
Author(s):  
Andrey V. Tsiganov
Keyword(s):  
Chaplygin Ball ◽  
Integrable Discretization

scholarly journals Chaplygin ball over a fixed sphere: an explicit integration

2008 ◽  
Vol 13 (6) ◽  
pp. 557-571 ◽  
Author(s):  
A. V. Borisov ◽  
Yu. N. Fedorov ◽  
I. S. Mamaev
Keyword(s):  
Explicit Integration ◽  
Chaplygin Ball

scholarly journals On some new forms of lattice integrable equations

Open Physics ◽  
2014 ◽  
Vol 12 (5) ◽  
Author(s):  
Corina Babalic ◽  
Adrian Carstea
Keyword(s):  
Bilinear Form ◽  
Gordon Equation ◽  
Discrete Systems ◽  
Travelling Wave ◽  
Higher Order ◽  
Sine Gordon Equation ◽  
Integrable Discretization ◽  
Miura Transformations ◽  
Hirota Bilinear ◽  
Wave Reduction

AbstractInspired by the forms of delay-Painleve equations, we consider some new differential-discrete systems of KdV, mKdV and Sine-Gordon — type related by simple one way Miura transformations to classical ones. Using Hirota bilinear formalism we construct their new integrable discretizations, some of them having higher order. In particular, by this procedure, we show that the integrable discretization of intermediate sine-Gordon equation is exactly lattice mKdV and also we find a bilinear form of the recently proposed lattice Tzitzeica equation. Also the travelling wave reduction of these new lattice equations is studied and it is shown that all of them, including the higher order ones, can be integrated to Quispel-Roberts-Thomson (QRT) mappings.

On an integrable discretization of integrable systems with a separatrix

1998 ◽  
Vol 250 (4-6) ◽  
pp. 300-310 ◽  
Author(s):  
Yukitaka Minesaki ◽  
Yoshimasa Nakamura
Keyword(s):  
Integrable Systems ◽  
Integrable Discretization
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