# tailieunhanh - Handbook of mathematics for engineers and scienteists part 105

## Handbook of mathematics for engineers and scienteists part 105. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | 696 Nonlinear Partial Differential Equations Here for simplicity the formulas are written out for the case of a second-order differential operator. For higher-order operators the right-hand sides of relations will contain higher-order derivatives of . The functionals and functions 1 X . X QT x . pn x together are assumed to be linearly independent and the Aj C are linearly independent functions of C1 . Cn. The basis functions are determined by solving the usually overdetermined system of ordinary differential equations j z 1 1 Q . n n v n Pj 1F1 Pj 2P2 Pj nPn j 1 . k where pj i are some constants independent of the parameters C1 . Cn. If for some collection of the constants pij system is solvable in practice it suffices to find a particular solution then the functions pi pi x define a linear subspace invariant under the nonlinear differential operator . In this case the functions appearing on the right-hand side of are given by fi C1 . Cn P1 iA1 C1 . Cn P2 iA2 C1 . Cn PkA C1 . Cn Bi C1 . Cn . Remark. The analysis of nonlinear differential operators is useful to begin with looking for twodimensional invariant subspaces of the form Z2 1 q x . Proposition 1. Let a nonlinear differential operator F w admit a two-dimensional invariant subspace of the form C 2 1 p x where p x Pp1 x qp2 x P and q are arbitrary constants and the functions 1 p1 x P2 x are linearly independent. Then the operator F w also admits a three-dimensional invariant subspace 2 2 1 p1 x p2 x . Proposition 2. Let two nonlinear differential operators F1 w and F2W admit one and the same invariant subspace 2 n 1 x . pn x . Then the nonlinear operator PF1 w qF2 w where p and q are arbitrary constants also admits the same invariant subspace. Example 3. Consider the nonlinear differential operator . We look for its invariant subspaces of the form iZ2 1 q x . We have F C1 C2Q x F. . kQ2 C2 a A kC2 bC c bC2 2kC C2 q. Here l i X qX 2 kQ2 and E X a Xx. .

TÀI LIỆU LIÊN QUAN
4    68    0
24    189    2
77    318    10
132    101    3
11    125    0
90    156    9
97    140    1
3    64    2
63    83    1
63    119    1
TÀI LIỆU XEM NHIỀU
8    460197    47
14    12397    36
13    9230    483
3    8201    102
14    7983    416
8    6781    2142
16    6755    397
249    5883    980
7    4676    3
17    4524    195
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
20    90    0    01-02-2023
34    95    0    01-02-2023
5    118    0    01-02-2023
16    103    0    01-02-2023
108    91    0    01-02-2023
10    85    0    01-02-2023
2    99    0    01-02-2023
12    105    0    01-02-2023
14    83    0    01-02-2023
6    90    0    01-02-2023
TÀI LIỆU HOT
8    6781    2142
112    2541    1120
249    5883    980
561    1871    574
152    2109    518
122    2639    491
13    9230    483
62    1963    481
35    2738    436
14    7983    416
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.