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Funktsional. Anal. i Prilozhen., 1988, Volume 22, Issue 1, Pages 23–33 (Mi faa1082)  

This article is cited in 27 scientific papers (total in 27 papers)

Two-dimensional “inverse scattering problem” for negative energies and generalized-analytic functions. I. Energies below the ground state

P. G. Grinevich, S. P. Novikov

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English version:
Functional Analysis and Its Applications, 1988, 22:1, 19–27

Bibliographic databases:

UDC: 517.957+512.7
Received: 19.02.1987

Citation: P. G. Grinevich, S. P. Novikov, “Two-dimensional “inverse scattering problem” for negative energies and generalized-analytic functions. I. Energies below the ground state”, Funktsional. Anal. i Prilozhen., 22:1 (1988), 23–33; Funct. Anal. Appl., 22:1 (1988), 19–27

Citation in format AMSBIB
\by P.~G.~Grinevich, S.~P.~Novikov
\paper Two-dimensional ``inverse scattering problem'' for negative energies and generalized-analytic functions. I. Energies below the ground state
\jour Funktsional. Anal. i Prilozhen.
\yr 1988
\vol 22
\issue 1
\pages 23--33
\jour Funct. Anal. Appl.
\yr 1988
\vol 22
\issue 1
\pages 19--27

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    This publication is cited in the following articles:
    1. R. G. Novikov, G. M. Henkin, “The $\bar\partial$-equation in the multidimensional inverse scattering problem”, Russian Math. Surveys, 42:3 (1987), 109–180  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. R. G. Novikov, “Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$”, Funct. Anal. Appl., 22:4 (1988), 263–272  mathnet  crossref  mathscinet  zmath  isi
    3. P. G. Grinevich, “Rapidly decreasing potentials on a background of finite-zone potentials and the $\partial$-problem on Riemann spaces”, Funct. Anal. Appl., 23:4 (1989), 321–322  mathnet  crossref  mathscinet  zmath  isi
    4. Theoret. and Math. Phys., 99:2 (1994), 599–605  mathnet  crossref  mathscinet  zmath  isi
    5. T. I. Garagash, A. K. Pogrebkov, “Scattering problem for the differential operator $\partial_x\partial_y+1+a(x,y)\partial_y+ b(x,y)$”, Theoret. and Math. Phys., 102:2 (1995), 117–132  mathnet  crossref  mathscinet  zmath  isi
    6. P. G. Grinevich, “Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity”, Russian Math. Surveys, 55:6 (2000), 1015–1083  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. I. A. Taimanov, S. P. Tsarev, “Two-dimensional Schrödinger operators with fast decaying potential and multidimensional $L_2$-kernel”, Russian Math. Surveys, 62:3 (2007), 631–633  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. I. A. Taimanov, S. P. Tsarev, “Two-dimensional rational solitons and their blowup via the Moutard transformation”, Theoret. and Math. Phys., 157:2 (2008), 1525–1541  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Building an extended resolvent of the heat operator via twisting transformations”, Theoret. and Math. Phys., 159:3 (2009), 721–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. I. A. Taimanov, S. P. Tsarev, “On the Moutard transformation and its applications to spectral theory and soliton equations”, Journal of Mathematical Sciences, 170:3 (2010), 371–387  mathnet  crossref  mathscinet
    11. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “The equivalence of different approaches for generating multisoliton solutions of the KPII equation”, Theoret. and Math. Phys., 165:1 (2010), 1237–1255  mathnet  crossref  crossref  adsnasa  isi
    12. V. G. Dubrovskii, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions with functional parameters of the Nizhnik–Veselov–Novikov equation with constant asymptotic values at infinity”, Theoret. and Math. Phys., 165:2 (2010), 1470–1489  mathnet  crossref  crossref  isi
    13. V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions of two-dimensional integrable equations using the $\bar\partial$-dressing method”, Theoret. and Math. Phys., 167:3 (2011), 725–739  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    14. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Properties of the solitonic potentials of the heat operator”, Theoret. and Math. Phys., 168:1 (2011), 865–874  mathnet  crossref  crossref  mathscinet  isi
    15. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Extended resolvent of the heat operator with a multisoliton potential”, Theoret. and Math. Phys., 172:2 (2012), 1037–1051  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    16. A. V. Kazeykina, “Absence of Conductivity-Type Solitons for the Novikov–Veselov Equation at Zero Energy”, Funct. Anal. Appl., 47:1 (2013), 64–66  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. I. A. Taimanov, S. P. Tsarev, “Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation”, Theoret. and Math. Phys., 176:3 (2013), 1176–1183  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. A. V. Kazeykina, “Absence of Solitons with Sufficient Algebraic Localization for the Novikov–Veselov Equation at Nonzero Energy”, Funct. Anal. Appl., 48:1 (2014), 24–35  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. P. G. Grinevich, A. E. Mironov, S. P. Novikov, “On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator”, Russian Math. Surveys, 70:2 (2015), 299–329  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    20. Klein Ch., Saut J.-C., “IST Versus PDE: A Comparative Study”, Hamiltonian Partial Differential Equations and Applications, Fields Institute Communications, eds. Guyenne P., Nicholls D., Sulem C., Springer, 2015, 383–449  crossref  mathscinet  zmath  isi
    21. Grinevich P.G., Novikov R.G., “Moutard Transform for Generalized Analytic Functions”, J. Geom. Anal., 26:4 (2016), 2984–2995  crossref  mathscinet  zmath  isi  scopus
    22. Grinevich P.G., Novikov R.G., “Moutard transform approach to generalized analytic functions with contour poles”, Bull. Sci. Math., 140:6 (2016), 638–656  crossref  mathscinet  zmath  isi  elib  scopus
    23. E. L. Lakshtanov, B. R. Vainberg, “A test for the existence of exceptional points in the Faddeev scattering problem”, Theoret. and Math. Phys., 190:1 (2017), 77–90  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    24. P. G. Grinevich, S. P. Novikov, “Singular solitons and spectral meromorphy”, Russian Math. Surveys, 72:6 (2017), 1083–1107  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    25. R. G. Novikov, I. A. Taimanov, “Darboux–Moutard transformations and Poincaré–Steklov operators”, Proc. Steklov Inst. Math., 302 (2018), 315–324  mathnet  crossref  crossref  mathscinet  isi  elib
    26. Music M. Perry P., “Global Solutions For the Zero-Energy Novikov-Veselov Equation By Inverse Scattering”, Nonlinearity, 31:7 (2018), 3413–3440  crossref  mathscinet  zmath  isi  scopus
    27. Grinevich P.G. Novikov R.G., “Creation and Annihilation of Point-Potentials Using Moutard-Type Transform in Spectral Variable”, J. Math. Phys., 61:9 (2020), 093501  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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