A. I. Bobenko, D. A. Kubenskii, “Qualitative analysis and calculations of finite-gap solutions of the Korteweg–de Vries equation. Automorphic approach”, TMF, 72:3 (1987), 352–360; Theoret. and Math. Phys., 72:3 (1987), 929

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Teoreticheskaya i Matematicheskaya Fizika, 1987, Volume 72, Number 3, Pages 352–360 (Mi tmf5336)

This article is cited in 9 scientific papers (total in 9 papers)

Qualitative analysis and calculations of finite-gap solutions of the Korteweg–de Vries equation. Automorphic approach

A. I. Bobenko, D. A. Kubenskii

Full-text PDF (893 kB) Citations (9)

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Abstract: The Schottky uniformisation theory is used to obtain new formulas for the characteristics of finite-gap solutions of the KdV equation. Waive number phase velocities and amplitudes are expressed in terms of Poincare series. Numerical results obtained by the method proposed are presented.

Received: 27.03.1986

English version:
Theoretical and Mathematical Physics, 1987, Volume 72, Issue 3, Pages 929–935
DOI: https://doi.org/10.1007/BF01018298

Bibliographic databases:

Language: Russian

Citation: A. I. Bobenko, D. A. Kubenskii, “Qualitative analysis and calculations of finite-gap solutions of the Korteweg–de Vries equation. Automorphic approach”, TMF, 72:3 (1987), 352–360; Theoret. and Math. Phys., 72:3 (1987), 929–935

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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Linking options:

https://www.mathnet.ru/eng/tmf5336

https://www.mathnet.ru/eng/tmf/v72/i3/p352

This publication is cited in the following 9 articles:

A.R. Osborne, “Rogue waves: Classification, measurement and data analysis, and hyperfast numerical modeling”, Eur. Phys. J. Spec. Top., 185:1 (2010), 225
International Geophysics, 97, Nonlinear Ocean Waves and the Inverse Scattering Transform, 2010, 877
Alfred R. Osborne, International Geophysics, 97, Nonlinear Ocean Waves and the Inverse Scattering Transform, 2010, 353
A. R. Osborne, M. Petti, “Laboratory-generated, shallow-water surface waves: Analysis using the periodic, inverse scattering transform”, Physics of Fluids, 6:5 (1994), 1727
A. R. Osborne, “Numerical construction of nonlinear wave-train solutions of the periodic Korteweg–de Vries equation”, Phys. Rev. E, 48:1 (1993), 296
North-Holland Mathematics Studies, 167, Topics in Soliton Theory, 1991, 397
A.I. Bobenko, S.B. Kuksin, “Finite-gap periodic solutions of the KdV equation are non-degenerate”, Physics Letters A, 161:3 (1991), 274
A.R. Osborne, E. Segre, “Numerical solutions of the Korteweg-de Vries equation using the periodic scattering transform μ-representation”, Physica D: Nonlinear Phenomena, 44:3 (1990), 575
A. I. Bobenko, L. A. Bordag, “Qualitative analysis of finite-gap solutions of the Kg? equation by the automorphic approach”, J Math Sci, 50:6 (1990), 1951

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

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Abstract page:	323
Full-text PDF :	130
References:	61
First page:	1

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