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( - )
 
2006

631.6; 626/627; 631.3

 

.. ...,

. ,

..

BSM, . ,

 

, (2,3,4), , , . .

(1,2,3) (4).

, , . , , , , . (1),(2),(3), 4/3q1y11 . . , . : ; , , , ; , . , , . , .

, , . , , . , , ( ), , .

:

;

(, );

;

;

.

, , , , , .

:

y0!! + q12 / (3h2) 4/3 q1y0! +4/3 h2y02 +y02/6 +y0/3 q12 / (3h2h1) = 0; (1)

y1!! 4/3q1y1! + 8/3h2y0!y1! y02γ1/(6h02) + y0y1 + y1/3 = 0; (2)

y2!! 4/3q1y2! + 4/3h2y12 + 8/3h2y0!y2! y02γ2/(6h02) + y02γ12/(12h04) y0y1γ1/(3h02)

y12/6 + y2/3 = 0, (3)

, , , , ĥ2 ; h ; q1 , μ (μ = 1/ĥ2).

, , t t+Δt . , .

, . , .

, (1, 2, 3).

, y . .

y! = 0,

y(0) = A, y!(0) = 0,

y = yo + μy1 + μ2y2 + . . . ,

(. (2)),

y0(0) + μy1(0) + μ2y2(0) = A;

ŷ0(0) + μŷ1(0) + μ2ŷ2(0) = 0. (4)

(4), μ :

y0(0) = 0, y10(0) = 0; (5)

y1(0) = 0, y11(0) = 0; (6)

y2(0) = 0, y12(0) = 0. (7)

(1), (5), (6), (7),

y0 = A cos (t/3). (8)

(8) (2), :

y!!1 + y1/3 = 4/3q1y!1 8/3ħ2y!0y!1 + (y20γ1)/(6ħ20) y0y1/3. (9)

(8), :

y!!1+ y1/3 = 4/3 q1y!1 + 8/3 ĥ2y!1Asin(t/3) + (A2cos2t/3) γ1/6/ĥ20 A/3cos(t/3)y1; (10)

y!!1 + y1/3 4/3 q1y!1 = γ1/6/ĥ20 y20; (11)

y!!1 + y1/3 4/3 q1y!1 = A2 γ1/(6ħ20) cos2(t/3); (12)

(D21 4/3 q1D + 1/3) y = A2 γ1/(6ħ20) cos(t/3), (13)

y = A2 γ1 / (6ħ20 (D21-4/3 q1D + 1/3)) cos2(t/3), (14)

D1,2 = 4/6 q1 (16/36 q21 1/3);

y1,2 = 4/6 q1 (16/36 q21 1/3).

, :

y!!2 4/3 q1y!2 + 4/3 ĥ2 (4/6 q1 + √ (16/36 q21 1/3))2 8/3ĥ2 A sin(t/3) y!2

A2 cos2(t/3) γ2 /(6ĥ20) + A2 cos2(t/3) γ21 /(12ĥ40) A cos(t/3) (4/6 q1 √ 16/36 q21 -

1/3) γ1 /(3ĥ20) 1/6 (4/6 q1 16/36 q21 1/3)2 + y2/3 = 0. (15)

(15),

y!!2 (4/3 q1 + 8/3 ĥ2 A sin(t/3)) y!2 + 1/3 y2 = (1/6 4/3 ĥ2) (4/6 q1 + √16/36 q21 1/3).

y = D, :

y2 (D22 (4/3 q1 + 8/3 ĥ2 A sin(t/3)) D + 1/3) = (1/6 4/3 ĥ2) (4/6 q1 + √16/36 q21 1/3),

y2 = (1/6 4/3 ĥ2) (4/6 q1 + √16/36 q21 1/3) / (D22 (4/3q1 + 8/3ĥ2A sin(t/3)D + 1/3),

D1-2 = 2/3 q1 + 4/3 ĥ2 A sin(t/3) √(q1 + 4/3 ĥ2 A sin(t/3))2 1/3,

2 = ((1-12ĥ2)/6 (4/6 q1 + √16/36 q21 1/3)) / (2/3 q1 +4/3 ĥ2 A sin(t/3)

(2/3 q1 + 4/3 ĥ2 A sin(t/3))2 1/3).

 

y = A cos(t/3) + μ (4/6 q1 √ 16/36q21 1/3) + μ2 (((1-12 ĥ2) (4/6 q1 + √16/36q21 1/3))/

(2/3 q1 + 4/3 ĥ2 A sin(t/3) √ (2/3 q1 +4/3 ĥ2 A sin(t/3))2 1/3 ). (16)

 

.

, ( ).

 

 

1.      .. . . : - , 1995.

2.      .. .. . /. - .,. 2003. . 136-137.

3.      .. .. . /. - . ., 2003. . 137-138.

4.      .. .. . /. - . .: , 2004. . 196-199.

5.      .. . .: , 1969.

6.      .. . .: , 2003.

7.      ., . , . .-: , 2002.

8.      .., .. . .: - , 1955.

9.      . . . .: , 1972.

10.  .., . . .-: , 2004.