scholarly journals Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation

2014 ◽  
Author(s):  
Ling-Ling Xue
Keyword(s):  
Kdv Equation ◽  
Darboux Transformations ◽  
Super Kdv Equation

scholarly journals Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation

2010 ◽  
Vol 466 (2120) ◽  
pp. 2471-2493 ◽  
Author(s):  
C. X. Li ◽  
J. J. C. Nimmo
Keyword(s):  
Kdv Equation ◽  
Difference Operators ◽  
Darboux Transformations ◽  
Standard Case ◽  
New Approach ◽  
Link Type ◽  
Special Cases ◽  
Super Kdv Equation ◽  
The One ◽  
Generalized Type

This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation D satisfying D ( AB )= D ( A )+ σ ( A ) B where σ is a homomorphism. Such twisted derivations include regular derivations, difference and q -difference operators and superderivatives as special cases. Remarkably, the formulae for the iteration of Darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants. As an example, we revisit the Darboux transformations for the Manin–Radul super KdV equation, studied in Liu and Mañas (Liu & Mañas 1997 a Phys. Lett. B 396 , 133–140 ( doi:10.1016/S0370-2693(97)00134-2 )). The new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants, covering all cases at once, rather than using several subcases. Then, by using a known relationship between quasideterminants and superdeterminants, we obtain expressions for these solutions as ratios of superdeterminants. This coincides with the results of Liu and Mañas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression. Finally, we obtain another type of quasideterminant solution to the Manin–Radul super KdV equation constructed from its binary Darboux transformations. These can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary Darboux transformations in earlier work on this topic.

Towards an integrable N=3 super KdV equation

1993 ◽  
Vol 173 (2) ◽  
pp. 143-147
Author(s):  
Stefano Bellucci ◽  
Evgenyi Ivanov ◽  
Sergey Krivonos
Keyword(s):  
Kdv Equation ◽  
Super Kdv Equation

Similarity solutions of the super KdV equation

1995 ◽  
Vol 16 (9) ◽  
pp. 901-904 ◽  
Author(s):  
Yu Huidan ◽  
Zhang Jiefang
Keyword(s):  
Kdv Equation ◽  
Similarity Solutions ◽  
Super Kdv Equation

Symmetries for the super-KdV equation

1988 ◽  
Vol 21 (11) ◽  
pp. L579-L584 ◽  
Author(s):  
P H M Kersten ◽  
P K H Gragert
Keyword(s):  
Kdv Equation ◽  
Super Kdv Equation

Darboux Transformations via Lie Point Symmetries: KdV Equation

2014 ◽  
Vol 31 (1) ◽  
pp. 010201 ◽  
Author(s):  
Yu-Qi Li ◽  
Jun-Chao Chen ◽  
Yong Chen ◽  
Sen-Yue Lou
Keyword(s):  
Kdv Equation ◽  
Lie Point Symmetries ◽  
Darboux Transformations
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