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Coupled Nonlinear Schrödinger Equations and the Miura Transformation

Chinese Physics Letters, 2011
A wide class of coupled nonlinear Schrodinger (NLS) equations are derived by virtue of the dressing method, and the associated parametric solutions are discussed. As an illustration, the explicit solution of the coupled NLS-type equation associated with σ1 is given.
Yan Lou, Jun-Yi Zhu
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The discrete Painlev  II equations: Miura and auto-B cklund transformations

Journal of Physics A: Mathematical and General, 2003
This paper deals with the Miura transformations for all discrete Painlevé II equations known up to date. Based on these transformations the authors derive special solutions in terms of discrete Airy functions and construct auto-Bäcklund transformations for the discrete Painlevé equations.
Carstea, A. S.   +3 more
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New Miura type transformations between integrable dispersive wave equations

Communications in Nonlinear Science and Numerical Simulation, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yin, Jiuli, Tian, Lixin, Wang, Lixia
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Equivalent classes of integrable nonlinear evolution equations and generalised Miura transformations

Journal of Physics A: Mathematical and General, 1987
We write down the recursion operator which defines the class of integrable nonlinear evolution equations (NEE) associated with a spectral problem (SP) for matrices of rank 2 depending quadratically on the spectral parameter. Then we show the existence of four different transformations which transform the given SP into the well known one of Zakharov and
CHEN DY, LEVI, Decio, LI YS
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Miura-ori enabled stretchable circuit boards

Npj Flexible Electronics, 2021
Yongkai Li, Weixuan Liu, Wei Hong
exaly  

On Miura transformations and Volterra-type equations

2008
We construct Miura transformations mapping the scalarspectral problems of the integrable lattice equations belonging tothe Adler-Bobenko-Suris (ABS) list into the discrete Schrodingerspectral problem associated with Volterra-type equations. We showthat the ABS equations correspond to Backlund transformations forsome particular cases of the discrete ...
PETRERA, Matteo   +3 more
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Miura transformations and symmetry groups of differential equations

1993
The main aim of this work is to develop a generalization of the Miura transformation based on symmetry groups of differential equations. Some applications of the resulting transformations are presented. The central idea is a construction, called an HC-projection, which will generalize the well known Hopf-Cole transformation.
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