Journal Name:
- Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi
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Abstract (2. Language):
In this paper we will consider two scalar di erential operators L and M. We
call them scalar because their coecients are functions rather than matrices.
Our aim is to obtain some gauge invariant equations. In order to achieve
this goal we rstly nd the gauge invariants of L and M by using the gauge
transformation on L and M. And then we apply `L-M-f triad' representation
[L;M] + fL = 0 which gives us some linear and nonlinear equations such as
the NV equation in invariant form.
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Abstract (Original Language):
Bu makalede L ve M'yi iki skaler diferansiyel operator olarak gozonune alaca~gz.
Burada L ve M skaler operatorlerdir, cunku bu operatorlerin katsaylar matrisler
de~gil fonksiyonlardr. Bizim amacmz 'gauge invariant' denklemlerini
elde etmektir. Bu amaca ulas.mak icin ilk once L ve M uzerinde 'gauge transformasyon'
kullanarak L ve M nin 'gauge invariant' larn bulaca~gz. Daha
sonra `L-M-f triad' denklemine, [L;M] + fL = 0 , bas.vurarak baz lineer ve
lineer olmayan, orne~gin Novikov-Veselov(NV), denklemleri invariant form'da
elde edilir.
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