nblib.library.kz - /elib/library.kz/jurnal/v_2006_1/

(1)

51

c

_R

-

.

. 2.

-

c = 100 -

, – 2 -

P

₀

. – (

₀

0 , 25 ,

10 508 ,

4

³

0

,

₀

7 10

³ ³

, c

_S₀

802 , 5 ),

– ( 0 , 2 , 2 , 5 10

³

,

10

3

5 ,

2

³

, c

_S

1006 , 4 ),

R = 3 , h=1,2R. -

,

.

, =0, -

.

1 ,

2, 3, 4 – -

– 2 , 5 , 10 . ,

. -

.

|y|

, |y| 2R -

.

1. . -

// - . 1984. 6. . 58-61.

2. ., ., . -

// . .

.- . , 1986. 5. . 75-80.

Summary

In persisting work is studied influence cylindrical on tense-deformed condition to day surface, at influence moving along axis of the subway twisting periodic load. Obdelka subway is prototyped by fine shell of the endless length, array – a springy uniform ambience. The contact between shell and ambience relies on slitherring Moving the shell is described by classical equations to theories fine shell, but surrounding ambiences – a dynamic equations to theories to bounce.

The decision is received for velocities of the movinging load, below critical. Under the numerical realization of the problem, for determination factor, is used method of the consequent reflections.

The Results calculation are presented in the manner of graph.

539.3:534.1

, . 2.04.06 .

.

1. .

, -

,

[1–5]. ,

,

- -

. ,

, -

.

, -

( .,

, [6]). , -

-

. ,

,

s E s kT

Z exp[ ( )( )

¹

] , k -

,

s , E(s) T – -

. ,

Z -

, .

-

( ): S t S S xx ,

(2)

52

2006. 1

1 ),

, ,

( S

₁

S

₂

S

₃

S

²

S . -

-

. – -

- ,

, , , .

- .

.

2. . -

(0+1)- -

. :

2 1

2

bv f

v u

u

_t

auw ,

2 2

2

bu f

v u

v

_t

avw ,

3 2

2

)

( c u v f

a

w

_t

. (1)

(1)

. ,

, , -

, .

, f

_i

= 0.

(1) -

:

u b v u c au bvw v

u a u

u

_tt

H

² ² ²

2

[ 2 ( )] ,

(2 ) v b v u c av buw v

u a v

v

_tt

H

² ² ²

2

[ 2 ( )] ,

(2 ) w

w a

w

_tt

H

²

, (2 ) . (1)

acw w

v

u )

t

2 (

² ² ²

. (3)

aw v

u )

_t

2 (

² ²

(4)

0 )

( u

²

v

²

w

²

c u

²

v

² _t

. (5)

) 4 ( 2

2 1 2 2 2

2

c

I c w

v

u . (6)

, -

(u,v,w) ,

(6), . .

. (1)

2

v

u aw w

w v v u R u

div (7)

v

t

u R

div (ln

² ²

) . (8)

, (1)

: F

H R R

R

_t _x _xx

, (9)

R = (u, v, w),

, u

, avw u

- auw

(

2 2 2 2

bu

v bv

v H

) ( )), u

( c

²

v

²

F f

_j

a . (10)

= 0, = 1 (1).

(2)

. ,

, (2) :

u = (c + d cos at) cos bt, v = (c + d cos at) sin bt,

w = d sin at. ,

.

3. .

. -

. ,

-

. -

, ,

, , .

,

.

- .

, , -

, , , , , -

, , , .

, .

(3)

53

,

.

. .

, ,

. -

, -

.

, .

. , ,

, ,

- .

-

. –

. -

, -

, , , , . .,

, - .

, , .

: )

,

2

X F ( X Y

D

X

_t _X

,

) ,

2

Y G ( X Y D

Y

_t _Y

, (11)

F, G – ;

D

_X

D

_Y

– -

.

) 1

2

X aX ( X

D

X

_t _X

, (12)

(3). 1+1 - )

1 ( X

X X

X

_t _yy

, (13) 1

a

D

_X

. -

- :

2 2 1 2 1 2

1

6 ) 5 6 ( exp 6 1

1 k y t

X . (14)

,

, .

,

(5). ,

] ) (

[ )

(

²

2 1 2

1 2

2 2 1 1

1

S

arctg S S

arctg S S S S

arctg S S

S

t yy y y

,

(15) X

S S

arctg (

₁ ₂ ¹

) . -

.

4. .

– .

: )

( ) 1

( cX F X

bX aX

X

_t _yy

. (16)

|

|y dt

de

X . .

N :

N

j

t e y j

e

j

t d X

1

)|

(

)

|

( . , -

. -

|

| 3

( y , t ) de

^y ^dt

S S ( y , t ) de

^|^y ^dt^| ⁱ ⁽^y^,^t⁾

.

5. .

– .

u, v, w

. -

, -

2

)

2

( u ,

, u ( x , y , z , , ) – -

. -

- )

, ,

( z .

² ² ² _z²

u

²

.

= 0

, ,

[7] C

ⁿ

( n k

² ²

n

²

)

ⁿ

e

^k² ² ⁿ² ⁱ⁽ⁿ ^kz⁾

. ,

.

6. . , , -

, ,

-

. -

, -

. -

-

.

(4)

54

2006. 1

1. . -

// . . .- . 2005. 3.

. 51-58.

2. Myrzakulov R. Solitons in biophysics. //

. 2005. 1. . 23-26.

3. . -

. 4- .

-

». , 2005. . 111.

4. .

// 59- . . .

, 2005. . 17.

5. ., ., .

// 4- . -

«

». , 2005.

. 107.

6. Sumners D.W. // Proc. Nath. Acad. Sci. USA. 2005. V. 102.

P. 9165-9169.

7. Wereszczynski A. // Mod. Phys. Lett. 2005. V. A20. P. 1135-1146.

: -

, . -

i . 1+1

i -

.

Summary

Some nonlinear processes in biology: chaos, solitons and patterns are considered. Exact soliton solutions of the generalized Fisher equation are found. The spin systems which is equivalent to the (1+1)-dimensional Fisher equation is constructed.