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Stable Solutions with Zeros to the Ginzburg–Landau Equation with Neumann Boundary Condition

✍ Scribed by Shuichi Jimbo; Yoshihisa Morita

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
796 KB
Volume
128
Category
Article
ISSN
0022-0396

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✦ Synopsis

This paper is devoted to the Ginzburg Landau equation 28+*(1& |8| 2 ) 8=0, 8=u 1 +iu 2 in a bounded domain 0/R n with the homogeneous Neumann boundary condition. The previous works [12 14] showed that for large * there exist stable non-constant solutions with no zeros in domains, which are topologically non-trivial in a certain sense. In this aritcle it is proved that for a domain 0 containing a non-trivial domain D as a subset, there exist stable solutions with zeros provided that the volume of 0"D is sufficiently small.

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