Affiliation:
1. Mathematics Department, Faculty of Science , Zagazig University , Zagazig , Egypt
Abstract
Abstract
In this paper, we studied the separability of the non-linear Schrodinger operator of the form
S
u
x
=
−
Δ
u
x
+
V
x
,
u
u
x
,
where
Δ
u
x
=
∑
i
=
1
n
∂
2
u
x
∂
x
i
2
,
$Su\left(x\right)=-{\Delta}u\left(x\right)+V\left(x,u\right)u\left(x\right),\,\text{where}\,{\Delta}u\left(x\right)={\sum }_{i=1}^{n}\frac{{\partial }^{2}u\left(x\right)}{\partial {x}_{i}^{2}},$
with the non-linear matrix potential
V
x
,
u
$V\left(x,u\right)$
. We obtained the sufficient conditions for separability of this operator in the space
L
2
R
n
ℓ
${L}_{2}{\left({R}^{n}\right)}^{\ell }$
and we established the suitable coercive inequalities.
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
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