The solution of the Liouville equation in the infinite limit
β Scribed by B. Leaf; W.C. Schieve
- Publisher
- Elsevier Science
- Year
- 1967
- Weight
- 553 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0031-8914
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π SIMILAR VOLUMES
We consider an equation &y"(x)+q(x) y(x)=f (x), x # R; ( 1 ) We study requirements for a weight function r(x) # L loc p (R) and for q(x) under which, for a given p # [1, ], regardless of f (x) # L p (R), the solution y(x) # L p (R) of Eq. (1) satisfies the inequalities:
dq N dp N Ο const, (3a) A numerical method for the time evolution of systems described by Liouville-type equations is derived. The algorithm uses a lattice of numerical markers, which follow exactly Hamiltonian trajectories, to represent the operator d/dt in moving (i.e., Lagrangian) coordinates. H