Positional stabilization of two-dimensional bilinear systems with degenerate matrix of the bilinear form

2000 ◽  
Vol 36 (9) ◽  
pp. 1423-1427
Author(s):  
S. K. Korovin ◽  
V. V. Fomichev ◽  
A. S. Shepit’ko
Keyword(s):  
Bilinear Form ◽  
Bilinear Systems ◽  
Two Dimensional ◽  
Degenerate Matrix

scholarly journals Controllability of two-dimensional bilinear systems

1996 ◽  
Vol 15 (2) ◽  
pp. 111-139 ◽  
Author(s):  
Carlos José Braga Barros ◽  
Joao Ribeiro Gonçalves Filho ◽  
Osvaldo Germano Do Rocío ◽  
Luiz A. B. San Martín
Keyword(s):  
Bilinear Systems ◽  
Two Dimensional

Symbolic Computation Study of a Generalized Variable-Coefficient Two-Dimensional Korteweg-de Vries Model with Various External-Force Terms from Shallow Water Waves, Plasma Physics, and Fluid Dynamics

2009 ◽  
Vol 64 (3-4) ◽  
pp. 222-228 ◽  
Author(s):  
Xing Lü ◽  
Li-Li Li ◽  
Zhen-Zhi Yao ◽  
Tao Geng ◽  
Ke-Jie Cai ◽  
...  
Keyword(s):  
Symbolic Computation ◽  
External Force ◽  
Bilinear Form ◽  
Water Waves ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Two Dimensional ◽  
Backlund Transformation ◽  
Bilinear Method ◽  
De Vries

Abstract The variable-coefficient two-dimensional Korteweg-de Vries (KdV) model is of considerable significance in describing many physical situations such as in canonical and cylindrical cases, and in the propagation of surface waves in large channels of varying width and depth with nonvanishing vorticity. Under investigation hereby is a generalized variable-coefficient two-dimensional KdV model with various external-force terms. With the extended bilinear method, this model is transformed into a variable-coefficient bilinear form, and then a Bäcklund transformation is constructed in bilinear form. Via symbolic computation, the associated inverse scattering scheme is simultaneously derived on the basis of the aforementioned bilinear Bäcklund transformation. Certain constraints on coefficient functions are also analyzed and finally some possible cases of the external-force terms are discussed

Oscillativity of Two-dimensional Bilinear Systems

2005 ◽  
Vol 66 (9) ◽  
pp. 1384-1395 ◽  
Author(s):  
V. N. Zhermolenko
Keyword(s):  
Bilinear Systems ◽  
Two Dimensional
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