Solutions of mKdV in Classes of Functions Unbounded at Infinity |
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| Authors: | T Kappeler P Perry M Shubin P Topalov |
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| Institution: | (1) Institute of Mathematics, University of Zürich, Winterthurer Strasse 190, 8057 Zürich, Switzerland;(2) Department of Mathematics, University of Kentucky, 719 Patterson Office Tower, Lexington, KY 40506-0027, USA;(3) Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, USA |
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| Abstract: | 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. |
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| Keywords: | KdV Modified KdV Spectra of Schr?dinger operators |
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