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

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Teoreticheskaya i Matematicheskaya Fizika, 1982, Volume 53, Number 2, Pages 163–180 (Mi tmf4373)

This article is cited in 20 scientific papers (total in 20 papers)

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

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

Full-text PDF (1672 kB) Citations (20)

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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.

Received: 07.04.1982

English version:
Theoretical and Mathematical Physics, 1982, Volume 53, Issue 2, Pages 1051–1062
DOI: https://doi.org/10.1007/BF01016674

Bibliographic databases:

Document Type: Article

Language: Russian

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

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

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\pages 163--180

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\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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Linking options:

https://www.mathnet.ru/eng/tmf4373

https://www.mathnet.ru/eng/tmf/v53/i2/p163

Cycle of papers

Application of inverse scattering method to singular solutions of nonlinear equations. I
V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov
TMF, 1982, 53:2, 163–180
Application of inverse scattering method to singular solutions of nonlinear equations. II
V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov
TMF, 1983, 54:1, 23–37
Application of inverse scattering method to singular solutions of nonlinear equations. III
V. A. Arkad'ev
TMF, 1984, 58:1, 38–49

This publication is cited in the following 20 articles:

A. A. Raskovalov, A. A. Gelash, “Resonanse interaction of breathers in the Manakov system”, Theoret. and Math. Phys., 213:3 (2022), 1669–1685
Mikhail Kovalyov, “Uncertainty principle for the nonlinear waves of the Korteweg–de Vries equation”, Chaos, Solitons & Fractals, 32:2 (2007), 431
M. Kovalyov, “On a class of solutions of KdV”, Journal of Differential Equations, 213:1 (2005), 1
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
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
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
M. Kovalyov, Mohammad Hosseini Ali Abadi, “An explicit formula for a class of solutions of the KdV equation”, Physics Letters A, 254:1-2 (1999), 47
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
A.B. Borisov, S.N. Ionov, “Vortices and vortex dipoles in 2D sine-Gordon model”, Physica D: Nonlinear Phenomena, 99:1 (1996), 18
R Beutler, A Stahlhofen, V B Matveev, “What do solitons, breathers and positons have in common?”, Phys. Scr., 50:1 (1994), 9
A A Stahlhofen, “Supertransparent potentials for the Dirac equation”, J. Phys. A: Math. Gen., 27:24 (1994), 8279
Theoret. and Math. Phys., 92:3 (1992), 952–963
V. O. Tarasov, “Boundary-value problem for the nonlinear Schr�dinger equation”, J Math Sci, 54:3 (1991), 958
I. T. Habibullin, A. G. Shagalov, “Numerical realization of the inverse scattering method”, Theoret. and Math. Phys., 83:3 (1990), 565–573
A.B. Borisov, “Vortices in the sine-Gordon system and solution of the boundary value problem by the inverse scattering transform”, Physics Letters A, 143:1-2 (1990), 52
P. N. Bibikov, V. O. Tarasov, “Boundary-value problem for nonlinear Schrödinger equation”, Theoret. and Math. Phys., 79:3 (1989), 570–579
V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Singular solutions of the KdV equation and the inverse scattering method”, J Math Sci, 31:6 (1985), 3264
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
A. Yu. Orlov, “N-soliton solution of chiral fields on Grassmann manifolds ($\sigma$ model)”, Theoret. and Math. Phys., 61:2 (1984), 1099–1107
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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