scholarly journals THE BIANCHI–DARBOUX TRANSFORM OF L-ISOTHERMIC SURFACES

2000 ◽  
Vol 11 (07) ◽  
pp. 911-924 ◽  
Author(s):  
EMILIO MUSSO ◽  
LORENZO NICOLODI
Keyword(s):  
Differential System ◽  
Darboux Transformation ◽  
Bäcklund Transformation ◽  
Linear Differential System ◽  
Backlund Transformation ◽  
Laguerre Geometry ◽  
Isothermic Surface ◽  
Isothermic Surfaces ◽  
Linear Differential ◽  
Darboux Transforms

We study an analogue of the classical Bäcklund transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi–Darboux transformation. First we show how to construct the Bianchi–Darboux transforms of an L-isothermic surface by solving an integrable linear differential system, then we establish a permutability theorem for iterated Bianchi–Darboux transforms.

scholarly journals On a linear differential system of neutral type

1986 ◽  
Vol 40 (2) ◽  
pp. 226-233
Author(s):  
P. Ch. Tsamatos
Keyword(s):  
Fixed Points ◽  
Differential System ◽  
Finite Dimension ◽  
Neutral Type ◽  
Common Fixed Points ◽  
Linear Differential System ◽  
Linear Differential

AbstractThis paper is concerned with the neutral type differential system with derivating arguments. By decomposing the space of initial functions into classes, it is derived that, for each class, the space of corresponding solutions is of finite dimension. The case of common fixed points of the arguments is also studied.

CHARACTERIZATIONS OF BIANCHI–BÄCKLUND TRANSFORMATIONS OF CONSTANT MEAN CURVATURE SURFACES

2005 ◽  
Vol 16 (02) ◽  
pp. 101-110 ◽  
Author(s):  
SHIMPEI KOBAYASHI ◽  
JUN-ICHI INOGUCHI
Keyword(s):  
Darboux Transformation ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Bäcklund Transformation ◽  
Bäcklund Transformations ◽  
Simple Type ◽  
Curvature Surface ◽  
Backlund Transformation ◽  
Constant Mean Curvature Surfaces ◽  
Constant Mean Curvature Surface

We show that Bianchi–Bäcklund transformation of a constant mean curvature surface is equivalent to the Darboux transformation and the simple type dressing.

scholarly journals The Research of Periodic Solutions of Time-Varying Differential Models

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Wenjun Liu ◽  
Yingxin Pan ◽  
Zhengxin Zhou
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Riccati Equations ◽  
Linear Differential System ◽  
Time Varying ◽  
Linear Differential

We have studied the periodicity of solutions of some nonlinear time-varying differential models by using the theory of reflecting functions. We have established a new relationship between the linear differential system and the Riccati equations and applied the obtained results to discuss the behavior of periodic solutions of the Riccati equations.

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