of integrable systems: say, the Harry-Dym equation. When the algebraic branch points appear, the ques- tion that follows is whether the model possesses the.
!" #$ % & "
Ý
! !
! " #$ " " "$ % "& # ' # # " "& " () * " ) + #, "& % # # # "& " " " # ) " " " " " " " # # &" "$ " ) &" " #, # " % " ' ) - % " ' " # # ) " % " # # " )" " ",
! !" # $ %$ & & ' ( ) ( & ( ' * + ,-, & & ( ' ( ' $ ( * . ( & ' ' ' %$ (* #' ( & ' ( ( ( (* / 0 1 2 03
4
,
( ( ' ) ' * 5 % ( ) ( ' * # ( 6 ( $ 0 2 03 7
4 4
, ,
-
, ,
- 8 -
-
- - 8
$ & ' 9 * :' 03 $ ' '% 03 , $ 4 4 "* / ( 03 ' 5(*; 8% ( ' ( ) ( ( ' * ' ( ( #03 03 $ $% ( *
# ( ' ( ( $ ' ( * / ? * 9 #' $6@5@ #5
( ? 2 :A3 $ ' ' * / .@/'@ ./ 6 ( :A3 % ( ? 2 A3 ' ( * / B % & 2 ./ ( * / ( * / '
' ' $ ) )* / 6 ( 1 * C '
) ) & $ ) & ) ( Æ $ ' ' * + $ ./ ( #03* 0
** '
4
4
32* " ($ & 4 , , 4 * / ( ) ( ' ' $ ' ( ( #03* + $ #03 * / % ( ( ( ' 7 D@A 2 * . ' ' 2 ( $ $ $% & ' B % * / $% ( ( ' $ $ ' ' ( $ ' ' $ ' ( * 9 $ #03 $% * / ( $ 4
E
' 32* E 32* "
4 4
- F
!
E
/ & ' ( 2 G $ ) & ' ' ( 4 4
4
½
4
F
H
½
::
' 4 )7;
$ ( ( 4 4 * +( ' ' $ ' ( ' G ( ? 2 & * / ' $ ' ( ' ( ' 32* G * '
,
32* G $ , ,, 4 4 , 4 4
$ ' ( ( * I$ ' 32* H $ 32* ,, 32* G $ ' ( ( 7
- , 4 , - 4
$
, ,!
( * 9 32* , ,! $ %$ ( '
- ,
4 - , **
4 ,
4
," ,8
4
4
"
,F
-
,H
/ % ' 4 $ $ $ 2 ( ' Æ ( 32* ,E ,G 6
-
" - 4
- "
4
,
+ ($ 32* & ' ( 32* ,F * 9 32*
' $ (* + $ ( 4 & * / $ G #03 03 $% *
!"
# ( #03 "
4 - " - " - ! - ! 4 - - -
! 32* " ( (
-
"
$ ' & * / ( & ( #03 & ( 32* ! * C & ' ( #03 @
- "
- " - 4 ,E -
- ; - " - < - 4 ,G -
& ( 6
/ 4 , ' ( ( ' ( 4 & * / % 4 $ $ $ & ($ ( 32* G ( ' ( ) F H $ 32* ,,
1"" ? < =6> "- F ? ;$ 0 ) D : => ( 3 @ 2" ; 6
=:> ( 3 @ E 0 : # $%& '() # ( 8 0 ) " : => 2 G" EG ? :
=> 2 G" : => '" 0 B => '" 0 B '6 =>
5 6: =>
5 0
" 3 : => @ ;$ " ? 2 3 :
=6> ; " ?$ EG ? ? - : => 2" : : =:> G ) 6
: => $ 3 " ( (" :
=> '" 0 B : * + => 2 2 ' $ ) A B '" 0 B 5 66 => B) ; 0 '" 0 B
6: => '" 0 B
=> J ; ,
0 ) $ / B"G => ( 3 @ E 0 : #
( 8 0 ) =6> '" 0 B
6
'
'
=> 3 2 D
# / -
B"G8 0 )
