Theoretical and Mathematical Physics

, Volume 157, Issue 2, pp 1525–1541 | Cite as

Two-dimensional rational solitons and their blowup via the moutard transformation

  • I. A. TaimanovEmail author
  • S. P. Tsarev


We construct a family of two-dimensional stationary Schrödinger operators with rapidly decaying smooth rational potentials and nontrivial L2 kernels. We show that some of the constructed potentials generate solutions of the Veselov-Novikov equation that decay rapidly at infinity, are nonsingular at t = 0, and have singularities at finite times t ≥ t0 > 0.


two-dimensional Schrödinger operator Moutard transformation Veselov-Novikov equation solution blowup 


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Copyright information

© MAIK/Nauka 2008

Authors and Affiliations

  1. 1.Institute of MathematicsNovosibirskRussia
  2. 2.Krasnoyarsk State Pedagogical UniversityKrasnoyarskRussia

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