Propagation of regularity and persistence of decay for fifth order dispersive models

This paper considers the initial value problem for a class of fifth order dispersive models containing the fifth order KdV equation $${\mathrm{\partial }}_{t}u-{\mathrm{\partial }}_x^{5}u-30u^2{\mathrm{\partial }}_{x}u+20{\mathrm{\partial }}_{x}u{\mathrm{\partial }}_x^{2}u+10u{\mathrm{\partial }}_x^{3}u=0.$$ The main results show that regularity or polynomial decay of the data on the positive half-line yields regularity in the solution for positive times.