​Department of Mathematics and its Applications

We implement an algorithm for the computation of Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems: Maple, Reduce and Mathematica. This class of Hamiltonian operators encompass almost all the examples coming from the theory of (1+1)-integrable evolutionary PDEs.

Integration of (9)–(10) with κ = 0 $\kappa=0$ , κ as in (20) and 10 times κ as in (20). Integration of (9) with initial datum as in (10) and the parameters described above. The three integrations differ in the choice of κ, which is assigned the value 0, the values in (20) and 10 times this latter value. The file names are: kappa0.avi corresponding to κ = 0; kappa1.avi corresponding to κ as in (20) kappa2.avi corresponding to 10 times the value of κ in (20). kappa3.avi corresponding to 20 times the value of κ in (20). (ZIP 2.2 MB)

Care Homes Integration. Integration of (9) with initial datum as in (11)–(13). The file name is CareHomes.avi. (ZIP 498 kB)

The Effects of Spatial Movements. Integration of (8) with initial datum as in (14). The case with spatial movement is in file MovingYes.avi, while the case with no movement is in MovingNo.avi. (ZIP 2.5 MB)