12
2006. 3
1. ., ., -
. . .: , 1959.
1084 .
2. . -
-
V // , . 2004. 5.
. 178-181.
3. ., . -
. .: , 1986. 544 .
4. . -
V
//
. , . . -
. , 2005. . II. . 236-238.
5. . . ., 2003. 431 .
V i i
, -
i i .
i i
i .
Summary
The task of synthesis of seven parameters of a spatial mechanism of V class upon set positions of input and output links is considered. The solving of excluding of unknown from a system of the power multinomials with the unknowns
621.01:531
. . . 17.03.06 .
. .
(2+1)-
1960- . ,
, -
,
, ,
[1,
c. 288–289]. -
- –
.
0
6 x xxx
t uu u
u (1)
, -
-
[2]. ,
(1+1) ( )
(1) -
( ., , [1–5]), -
.
1970 . [6] -
0 )
6
(uxxx u2 ux ut x uyy (2)
-
. 1976 . [7]
(2) -
. [8],
[9] (2)
. (2)
,
.
1988 . . . [10, . 188–189] -
-
u w v wu
vu u
u
ut xxx yyy y x ( y x) 2
) 1 ( )
( , (3)
y
x u
u 3( 2) , wy 3(u2)x. (4) (3), (4)
-
, -
(3), (4) .
[11] (2+1)- -
0
4 x V y VxU
xxy
t , (5)
13
x
Vy , Ux y, (6) [5, . 10–11]
- 0
) )(
(DyDt D2yD2x ,
n t m
xD F G
D ( )
t t x x n
t t m x
x ' ' F(x,t)G(x',t') ' ,' ,
(5), (6) - .
) , ,
(x y t – -
, .
, x
- x 1.
(5), (6) ) , ( )
, ,
(x y t t 0 0 x y , (7) )
,
0(x y – -
.
1965 . ,
(1) -
– . -
, , .
, -
, « » -
.
-
[3, c. 15]. -
, .
, . -
- - [12, . 2].
, - -
. -
,
, [12, . 2].
(2+1)- (5),
(6)
: 0
) , ,
(x y t x . (8)
, (2+1)-
(5), (6) (7) (8)
.
1.(2+1)- -
(5), (6) -
U0
x , (9) B
y A
t , (10)
) , (y t ,
0 0
U0 ,
2
1 , (11)
) ( ) ( 2
0
1 2 1
x y y x xy
A
0
) ( ) (
2 2 x1 y y1 x
xy , (12)
i i
i B i
y x x
y x x
) ( 2
) ( 2
1 1
1 1
, (13)
y
t . (14)
. ,
- (9), (10)
tx
xt ,
]) , [ (
]) , [
(U0t Ax U0 A U0y Bx U0 B
0 )
( t y , (15) [A, B] =AB –BA.
(15) :
0 ] , [ 0
0 A U A
U t x , (16)
0 ] , [ 0
0 B U B
U y x , (17)
y 0
t . (18)
(11)–(14) (17), (18) -
, (16)
(2+1)-
(5),(6). .
. , -
y t,
(9). x, .
) ,
(y t . ,
(15), (14).
14
2006. 3
2. (2+1)- -
(5), (6) U0
x , (19) B
y A
t
2 , (20) )
, (y t ,
0 0
U0 ,
2
1 , t y, (21)
) ( ) ( 2
0
1 2 1
x y y x xy
A
0
) ( ) (
2 2 x1 y y1 x
xy , (22)
i i
i B i
y x x
y x x
) ( 2
) ( 2
1 1
1 1
,(23)
i i
i C i
x
x 1
1
2
2 . (24)
. ,
- (19), (20)
tx xt
]) , [ (
]) , [
(U0t Ax U0 A U0y Bx BU0
0 ) (
]) , [
( 0
2
y t
x C U
C , (25)
[A, B] =AB –BA.
(15) :
0 ] , [ 0
0 A U A
U t x , (26)
0 ] ,
[ 0
0 B BU
U y x , (27)
0 ] , [CU0
Cx , (28)
y 0
t . (29)
(21)–(24) (27)–(29) -
, (26)
(2+1)- (5),
(6). .
3. (2+1)- -
(5), (6) U0
x , (30) D
B
y A
t
3
2 , (31)
) , (y t ,
0 0
U0 ,
2
1 , t y, (32)
) ( ) ( 2
0
1 2 1
x y y x xy
A
0
) ( ) (
2 2 x1 y y1 x
xy , (33)
i i
i B i
y x x
y x x
) ( 2
) ( 2
1 1
1 1
, (34)
i i
i D i
C
x
x 1
1
2
2 . (35)
. ,
- (30), (31)
tx
xt ,
]) , [ (
]) , [
(U0t Ax U0 A U0y Bx BU0
]) , [ ( ]) , [
( 0 3 0
2
x
x C U D DU
C
0 )
( t y , (36) [A, B] =AB –BA.
(36) :
0 ] , [ 0
0 A U A
U t x , (37)
0 ] ,
[ 0
0 B BU
U y x , (38)
0 ] , [C U0
Cx , (39) 0
] , [DU0
Dx , (40)
y 0
t . (41)
(32)–(35) (38)–(41) -
, (37)
(2+1)- (5),
(6). .
, -
, (2+1)-
(5)–(8):
1) B
U
y t
x 0
,
2) B C
U
y t
x
2
0 ,
15
3) B C D
U
y t
x
3 2
0 ,
. . . ………
( , ),y t
0 0
U0 ,
2 1
, t y,
) ( ) ( 2
0
1 2 1
x y y x xy
A
0
) ( ) (
2 2 x1 y y1 x
xy ,
i i
i B i
y x x
y x x
) ( 2
) ( 2
1 1
1 1
,
i i
i D i
C
x
x 1
1
2
... 2 .
(2+1)- (5)–(8)
.
1. ., ., ., . -
. ., 1988. 694 . 2.Washimi M., Taniuti T. Propagation of ion acoustic solitary waves of small amplitude // Phys. Rev. Lett. 1966.
V. 17. . 996-998.
3. ., .
. ., 1987. 477 c.
4. ., . -
. ., 1986. 527 .
5. . / .
. . . ., 1980. 319 .
6. ., .
// . . 1970. . 192. . 753-756.
7.Kako M., Rowland s G. Two dimensional stability of ion acoustic solitons // Plasma Physics. 1976. V. 18.
. 165-170.
8.Tappert F., Varma C.M. Asymptotic theory of self- trapping of heat pulses in solids // Phys. Rev. Lett. 1970. V. 25.
. 1108-1111.
9.Narayanamyrti V., Varma C.M. Nonlinear propagation of heat pulses in solids // Phys. Rev. Lett. 1970. V. 25. . 1105-1108.
10. . -
. , 1991. 232 .
11. . (2+1)-
// . . 6. 2001.
C. 5-11.
12. . . http://intra.rfbr.
ru/pub/knigi/janus/pe-linovskij/pelinovs.htm. 28.02.2001.
(2+1)- i i
. Summary
The hierarchy of the linear differential systems for the (2+1)-dimensional nonlinear Korteweg de Vries model is constructed.
517.95.958
, . 28.03.06 .
