Международная конференция студентов, аспирантов и Ð¼Ð¾Ð»Ð¾Ð´Ñ‹Ñ ...

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ko_fJha_g[jhdZdkbkl_fZf\b^Z
dzl
= Gl( z1, z2,... zN)
, l = 1,.. N
(3)
dt
N
A^_kv z = ( z , z ,..., z ) ∈C
Z g = g ( z , z ,..., z ) ∈ C ∞ –ZgZeblbq_kdb_ nmgdpbb dhfie_dk
1 2
N
l l 1 2 N
guoi_j_f_gguo z 1
, z 2
,..., z
N
.
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aZibkZggmx\nhjf_ijb]h^ghc^eydhfie_dkghagZqguoH>M
zˆ = z+ 0.5 ⋅τ( υ+ w) , ⎡⎣E− 0.5( 1 + i) τGz⎤⎦υ= f ( z, t+ 0.5 τ) , ⎡⎣E−0.5( 1 −i) τ Gz⎤⎦ w= f ( z, t+ 0.5 τ)
. (4)
A^_kv Gz
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2
kl\Zfb>@lhqghklv O( τ )
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j_gpbZevguchi_jZlhj
ut + uux =Λ u+ vuxx, (5)
]^_hi_jZlhj Λ hij_^_ey_lkyq_j_aij_h[jZah\Zgb_Nmjv_ihijhkljZgkl\_gghci_j_
f_gghc
+∞ +∞
u t x e u t k dk u t x e k u t k dk.
( , ) ikx
ikx
= ( , ) ; Λ ( , ) = ⋅ ( , )
∫
−∞
MjZ\g_gb_Kb\Zrbgkdh]hh[eZ^Z_lbgl_j_kgufk\hckl\hfdhlhjh_h[uqghgZ
au\ZxliheyjgufjZaeh`_gb_fpole decompositionZbf_gghmjZ\g_gb_(5)^himkdZ_l
j_r_gby\\b^_>@
2N
1
u( t, x)
=−2ν∑ (6)
x−z t
∫
−∞
α= 1 α
]^_ z α
ihexkZgZdhfie_dkghciehkdhklbijbqzfihexkZijbkmlkl\m_l\nhjfme_ (6)
dhfie_kghkhijy`zggufb iZjZfb >\b`_gb_ihexkh\ijhbkoh^blihke_^mxs_fmaZ
dhgm
1
z α
=−2ν∑
−i⋅sign( Imzα)
. (7)
z −z
β≠α α β
< kemqZ_ 2π-i_jbh^bqghklbihijhkljZgkl\_gghci_j_f_gghcfh`ghjZkkfZl
jb\ZlvlhevdhihexkZkj_ZevghcqZklvx Re z α
∈( 0,2π)
b\f_klhmjZ\g_gbc(6)b(7)bk
ihevah\Zlvke_^mxsb_mjZ\g_gby
()