The Eckhaus equation, which is a nonlinear Schrödinger type equation that can be linearized to the free linear Schrödinger 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 L2 norm of the solution is a constant of the motion. The ill-posedness disappears on the infinite line with square integrable data, but the solitonic solutions, which are not square integrable, are seriously unstable.
On the well posedeness of the Eckhaus equation
DE LILLO, Silvana
1997
Abstract
The Eckhaus equation, which is a nonlinear Schrödinger type equation that can be linearized to the free linear Schrödinger 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 L2 norm of the solution is a constant of the motion. The ill-posedness disappears on the infinite line with square integrable data, but the solitonic solutions, which are not square integrable, are seriously unstable.File in questo prodotto:
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