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The Eckhaus equation, which is a nonlinear Schrodinger type equation that can be linearized to the free linear Schrodinger equation, is considered. A linearized analysis of the nonlinear problem indicates that the periodic boundary value problem is ill-posed. The exact solution also demonstrates the ill-posedness, even though the L 2 norm of the solution is a constant of the motion. The...
The initial/boundary value problem for the Burgers equation on the semiline is solved with a flux-type boundary condition at the origin. Analytic solutions and asymptotic (large time) expansions are obtained for some cases of applicative relevance.
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