Using P. Lax's concept of a Lax pair we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and in particular, may tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schrödinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.
|Number of pages||35|
|Journal||Journal of Geometric Analysis|
|State||Published - Apr 2008|
Bibliographical noteFunding Information:
T. Kappeler supported in part by the Swiss National Science Foundation, the programme SPECT, and the European Community through the FP6 Marie Curie RTN ENIGMA (MRTN-CT-2004-5652). P. Perry partially supported by NSF-grant DMS-0408419. M. Shubin partially supported by NSF-grant DMS-0600196.
- Modified KdV
- Spectra of Schrödinger operators
ASJC Scopus subject areas
- Geometry and Topology