Tables of supersymmetric evolutionary equations with higher order symmetries

Supersymmetric evolution equations

Preliminary Comments

All weights mentioned in the tables below are based on a weight of x equal 2.

If casses are labeled as having weight(t)=n then this means that each term of the right hand side of f_t=... has the same weight as f_(n/2)x. Odd integer n weights can be obtained through the supersymmetric D derivative which has half of the weight of one x derivative. The highest x derivative may be lower than n/2 but each term has to have exactly this weight. In the evolutionary equations the weight is called weight(t) whereas in the symmetry it is called weight(s).

Only evolution equations and their symmetries are computed which satisfy the following non-triviality conditions:

If entries in tables are empty then the corresponding computations have not been completed yet.

So far the following cases have been considered:

Overview
weights: --> 123 45678 91011
N=1, 1 fermion field x x x x x x x x x x x



N=1, 1 fermion field f, weight 1
weight(s):-> 2345678 91011121314
weight(t): 1 _ _ _ _ _ _ _ _ _ _ _ _ _
2 _ 1 _ 1 _ 1 _ 1 _ 1 _ 1
3 _ _ _ _ _ _ _ _ _ _ _
4 _ 2 _ 4 _ 3 _ 3 _ 4
5 _ _ _ _ _ _ _ _ _
6 _ 3 _ 9 _ 5 _ 10
7 _ _ _ _ _ _ _
8 _ 6 _ 12 _
9 _ _ _ _ _
10 _ _
11 _ _ _
12 _
13 _


N=1, 1 fermion field f, weight 2
weight(s):> 2345678 91011121314
weight(t): 1 _
2 1 _ 1 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0
5 0 0 2 0 1 1 1 1 1
6 0 0 0 1 0 0 0 0
7 0 0 0 0 1 0 0
8
9
10
11
12
13


N=1, 1 fermion field f, weight 3
weight(s):> 2345678 91011121314
weight(t): 1 _ _ _ _ _ _ _ _ _ _ _ _ _
2 _ 0 _ 0 _ 0 _ 0 _ 0 _ 0
3 _ _ _ _ _ _ _ _ _ _ _
4 _ 0 _ 0 _ 0 _ 0 _ 0
5 _ _ _ _ _ _ _ _ _
6 _ 0 _ 3 _ 1 _ 4
7 _ _ _ _ _ _ _
8 _ 0 _ 1 _ 1
9 _ _ _ _ _
10 _ 1 _ 8
11 _ _ _
12 _ 2
13 _


N=1, 1 fermion field f, weight 4
weight(s):> 2345678 91011121314
weight(t): 1 _ _ _ _ _ _ _ _ _ _ _ _ _
2 _ _ 0 _ 0 _ 0 0 0 0 0 0
3 _ _ _ _ _ _ _ _ _ _ _
4 0 _ 0 _ 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0
6 0 _ 0 0 0 0 0 0
7 0 0 0 0 1 0 1
8 0 0 0 0 0 0
9 0 0 0 0 0
10 0 0 0 1
11 0 0 0
12 0 1
13 0


N=1, 1 fermion field f, weight 5
weight(s):> 2345678 91011121314
weight(t): 1
2
3
4
5
6
7
8
9
10
11
12
13


N=1, 1 fermion field f, weight 6
weight(s):> 2345678 91011121314
weight(t): 1
2
3
4
5
6
7
8
9
10
11
12
13


N=1, 1 fermion field f, weight 7
weight(s):> 2345678 91011121314
weight(t): 1
2
3
4
5
6
7
8
9
10
11
12
13


N=1, 1 fermion field f, weight 8
weight(s):> 2345678 91011121314
weight(t): 1
2
3
4
5
6
7
8
9
10
11
12
13


N=1, 1 fermion field f, weight 9
weight(s):> 2345678 91011121314
weight(t): 1
2
3
4
5
6
7
8
9
10
11
12
13


N=1, 1 fermion field f, weight 10
weight(s):> 2345678 91011121314
weight(t): 1
2
3
4
5
6
7
8
9
10
11
12
13


N=1, 1 fermion field f, weight 11
weight(s):> 2345678 91011121314
weight(t): 1
2
3
4
5
6
7
8
9
10
11
12
13



This page is maintained by

Thomas Wolf
E-mail:
twolf@brocku.ca