The multi-component (n+1)-dimensional vector nonlinear Scrodinger equation is as follows:
where is an m-vector of complex valued functions, and F is a real valued function of , t,. Before generating the system, we substituted = + i and seperated the original PDE into real and imaginary parts. This allowed us to work with a real system of equations, but in twice the number of depenent functions.
The determining system consists of the dependent variables 01a, 01b, ..., ma, mb, T and X01, X02,..., Xn which depend on the independent variables 01a, 01b, ..., ma, mb, t and x01, x02,..., xn. There is also the arbitrary function F(01a,01b,...,ma,mb, t, x01, x02,..., xn).
This class is extremely broad, but the determining systems for this fairly general class are available here (1.68 MB) for m = 1..4, n = 1..10 (the files in the archive are named vnlsfull_n_m).
The case for which we have provided benchmarks is for the following form of F:
Input | PureElim | ||||
Components | Dimension | Equations | Length | Time (sec) | Mem (MB) |
1 | 1 | 46 | 6097 | 0.03 | 0.78 |
1 | 2 | 120 | 13001 | 0.04 | 0.84 |
1 | 3 | 222 | 23093 | 0.06 | 0.86 |
1 | 4 | 352 | 36805 | 0.09 | 0.90 |
1 | 5 | 510 | 54569 | 0.17 | 0.98 |
1 | 6 | 696 | 76817 | 0.25 | 1.04 |
1 | 7 | 910 | 103981 | 0.37 | 1.15 |
1 | 8 | 1152 | 136493 | 0.52 | 1.21 |
1 | 9 | 1422 | 174785 | 0.80 | 1.36 |
1 | 10 | 1720 | 219289 | 1.17 | 1.64 |
Input | PureElim | ||||
Components | Dimension | Equations | Length | Time (sec) | Mem (MB) |
2 | 1 | 248 | 43955 | 0.34 | 1.13 |
2 | 2 | 624 | 84639 | 0.56 | 1.52 |
2 | 3 | 1144 | 142243 | 0.69 | 1.45 |
2 | 4 | 1808 | 218687 | 0.59 | 1.25 |
2 | 5 | 2616 | 315891 | 0.74 | 1.48 |
2 | 6 | 3568 | 435775 | 1.31 | 1.69 |
2 | 7 | 4664 | 580259 | 2.93 | 2.57 |
2 | 8 | 5904 | 751263 | 2.05 | 2.23 |
2 | 9 | 7288 | 950707 | 4.42 | 3.11 |
2 | 10 | 8816 | 1180511 | 3.94 | 2.76 |
Input | PureElim | ||||
Components | Dimension | Equations | Length | Time (sec) | Mem (MB) |
3 | 1 | 678 | 154665 | 1.67 | 1.90 |
3 | 2 | 1704 | 285333 | 1.84 | 1.97 |
3 | 3 | 3126 | 467037 | 2.03 | 2.12 |
3 | 4 | 4944 | 704817 | 2.70 | 2.16 |
3 | 5 | 7158 | 1003713 | 3.62 | 2.48 |
3 | 6 | 9768 | 1368765 | 5.19 | 3.27 |
3 | 7 | 12774 | 1805013 | 6.66 | 3.50 |
3 | 8 | 16176 | 2317497 | 9.43 | 3.74 |
3 | 9 | 19974 | 2911257 | 9.92 | 4.05 |
3 | 10 | 24168 | 3591333 | 27.30 | 6.28 |
Input | PureElim | ||||
Components | Dimension | Equations | Length | Time (sec) | Mem (MB) |
4 | 1 | 1408 | 394099 | 5.44 | 2.93 |
4 | 2 | 3552 | 709691 | 5.45 | 3.92 |
4 | 3 | 6528 | 1143347 | 14.45 | 7.54 |
4 | 4 | 10336 | 1705435 | 8.07 | 3.34 |
4 | 5 | 14976 | 2406323 | 20.77 | 5.57 |
4 | 6 | 20448 | 3256379 | 15.87 | 5.40 |
4 | 7 | 26752 | 4265971 | 27.77 | 5.90 |
4 | 8 | 33888 | 5445467 | 28.39 | 8.79 |
4 | 9 | 41856 | 6805235 | 67.25 | 10.03 |
4 | 10 | 50656 | 8355643 | 80.90 | 10.24 |