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 TMF, 1982, Volume 53, Number 2, Pages 163–180 (Mi tmf4373)

Application of inverse scattering method to singular solutions of nonlinear equations. I

V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov

Abstract: The Jost solutions and the transition matrix for the Zakharov–Shabat system are constructed in the case of potentials that have a finite number of $x^{-1}$ singularities. The analytic properties of the transition matrix are investigated and scattering data are introduced.

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English version:
Theoretical and Mathematical Physics, 1982, 53:2, 1051–1062

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Citation: V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Application of inverse scattering method to singular solutions of nonlinear equations. I”, TMF, 53:2 (1982), 163–180; Theoret. and Math. Phys., 53:2 (1982), 1051–1062

Citation in format AMSBIB
\Bibitem{ArkPogPol82}
\paper Application of inverse scattering method to singular solutions of nonlinear equations.~I
\jour TMF
\yr 1982
\vol 53
\issue 2
\pages 163--180
\mathnet{http://mi.mathnet.ru/tmf4373}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=693271}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 53
\issue 2
\pages 1051--1062
\crossref{https://doi.org/10.1007/BF01016674}

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This publication is cited in the following articles:
1. V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Application of inverse scattering method to singular solutions of nonlinear equations. II”, Theoret. and Math. Phys., 54:1 (1983), 12–22
2. V. A. Arkad'ev, “Application of inverse scattering method to singular solutions of nonlinear equations. III”, Theoret. and Math. Phys., 58:1 (1984), 24–32
3. A. Yu. Orlov, “N-soliton solution of chiral fields on Grassmann manifolds ($\sigma$ model)”, Theoret. and Math. Phys., 61:2 (1984), 1099–1107
4. P. N. Bibikov, V. O. Tarasov, “Boundary-value problem for nonlinear Schrödinger equation”, Theoret. and Math. Phys., 79:3 (1989), 570–579
5. I. T. Habibullin, A. G. Shagalov, “Numerical realization of the inverse scattering method”, Theoret. and Math. Phys., 83:3 (1990), 565–573
6. Theoret. and Math. Phys., 92:3 (1992), 952–963
7. S. Yu. Dobrokhotov, “Reduction of Hugoniot–Maslov chains for trajectories of solitary vortices of the “shallow water” equations to the Hill equation”, Theoret. and Math. Phys., 112:1 (1997), 827–843
8. Dobrokhotov, SY, “Hugoniot-Maslov chains for solitary vortices of the shallow water equations, I. - Derivation of the chains for the case of variable Coriolis forces and reduction to the Hill equation”, Russian Journal of Mathematical Physics, 6:2 (1999), 137
9. A. B. Borisov, “Asymptotic behavior of singular solitons and the inverse scattering method for solving boundary value problems”, Theoret. and Math. Phys., 124:2 (2000), 1094–1104
10. S. Yu. Dobrokhotov, “Integrability of truncated Hugoniot–Maslov chains for trajectories of mesoscale vortices on shallow water”, Theoret. and Math. Phys., 125:3 (2000), 1724–1741
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