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Infinitesimal Bäcklund Transformation and Conservation Laws for Non‐autonomous Systems
Author(s) -
Mahato G.,
Chowdhury A. Roy
Publication year - 1986
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19864980107
Subject(s) - infinitesimal , conservation law , transformation (genetics) , homogeneous space , korteweg–de vries equation , operator (biology) , soliton , mathematical physics , property (philosophy) , physics , infinity , mathematics , pure mathematics , mathematical analysis , nonlinear system , quantum mechanics , geometry , epistemology , repressor , transcription factor , gene , biochemistry , chemistry , philosophy
We have observed that it is possible to extend the concept of the infinitesimal Bäcklund transformation of Steudel to the case of non‐autonomous systems. We have discussed the situation with the cylindrical KdV as example. The interesting point to note is that though the B.T. for Ckdv does not possess the usual property of generating one soliton in a single operation, yet it generates an infinite number of symmetries, which corroborates with those obtained through the expansion of the resolvant of the linear operator associated with the equation.