Solutions of mKdV in classes of functions unbounded at infinity

Details Solutions of mKdV in classes of functions unbounded at infinity Solutions of mKdV in classes of functions unbounded at infinity

2006-01-11

arxiv.org/abs/math/0601237v4

Mathematics

Analysis of PDEs

35 pages, new results about spectra and eigenfunctions of Schr\"odinger operators added, new references added

Scientific paper

In 1974 P. Lax introduced an algebro-analytic mechanism similar to the Lax L-A pair. Using it 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 may even include functions which tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schr{\"o}dinger 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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