A. Degasperis, A. B. Shabat, “Construction of reflectionless potentials with infinite discrete spectrum”, TMF, 100:2 (1994), 230–247; Theoret. and Math. Phys., 100:2 (1994), 970

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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 100, Number 2, Pages 230–247 (Mi tmf1644)

This article is cited in 18 scientific papers (total in 18 papers)

Construction of reflectionless potentials with infinite discrete spectrum

A. Degasperis^a, A. B. Shabat^b

^a University of Rome "La Sapienza"
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Full-text PDF (1711 kB) Citations (18)

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Abstract: We investigate the one-dimensional Schrödinger operator. The condition that the potential be self-similar under Darboux transformation leads to transparent potentials with infinitely many eigenvalues.

Received: 04.02.1994

English version:
Theoretical and Mathematical Physics, 1994, Volume 100, Issue 2, Pages 970–984
DOI: https://doi.org/10.1007/BF01016760

Bibliographic databases:

Language: Russian

Citation: A. Degasperis, A. B. Shabat, “Construction of reflectionless potentials with infinite discrete spectrum”, TMF, 100:2 (1994), 230–247; Theoret. and Math. Phys., 100:2 (1994), 970–984

Citation in format AMSBIB

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\paper Construction of reflectionless potentials with infinite discrete spectrum

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\jour Theoret. and Math. Phys.

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\vol 100

\issue 2

\pages 970--984

\crossref{https://doi.org/10.1007/BF01016760}

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Linking options:

https://www.mathnet.ru/eng/tmf1644

https://www.mathnet.ru/eng/tmf/v100/i2/p230

This publication is cited in the following 18 articles:

Wansheng Wang, “High order stable Runge–Kutta methods for nonlinear generalized pantograph equations on the geometric mesh”, Applied Mathematical Modelling, 39:1 (2015), 270
Jianguo Si, Xianlong Li, “Small divisors problem in dynamical systems and analytic solutions of the Shabat equation”, Journal of Mathematical Analysis and Applications, 367:1 (2010), 287
M. Kh. Chankaev, A. B. Shabat, “A nonlinear eigenvalue problem”, Theoret. and Math. Phys., 157:2 (2008), 1514–1524
A. V. Domrin, “The Riemann Problem and Matrix-Valued Potentials with a Convergent Baker–Akhiezer Function”, Theoret. and Math. Phys., 144:3 (2005), 1264–1278
Willox, R, “Painlevé equations from Darboux chains: I. P-III-P-V”, Journal of Physics A-Mathematical and General, 36:42 (2003), 10615
V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661
A. B. Borisov, S. A. Zykov, “Reflectionless sine-Gordon potentials with an infinite spectrum”, Theoret. and Math. Phys., 118:3 (1999), 264–271
B. F. Samsonov, “On the $N$ -th order Darboux transformation”, Russian Math. (Iz. VUZ), 43:6 (1999), 62–65
W. Renger, “Toda Soliton Limits on General Backgrounds”, Journal of Differential Equations, 151:1 (1999), 191
Walter Renger, “A New Class of Soliton Solutions for the (Modified) Kadomtsev‐Petviashvili Equation”, Mathematische Nachrichten, 202:1 (1999), 125
Yunkang Liu, “Regular Solutions of the Shabat Equation”, Journal of Differential Equations, 154:1 (1999), 1
A. B. Borisov, S. A. Zykov, “The dressing chain of discrete symmetries and proliferation of nonlinear equations”, Theoret. and Math. Phys., 115:2 (1998), 530–541
Boris N Zakhariev, Vladimir M Chabanov, “New situation in quantum mechanics (wonderful potentials from the inverse problem)”, Inverse Problems, 13:6 (1997), R47
Vladislav G Bagrov, Boris F Samsonov, “Darboux transformation and elementary exact solutions of the Schrödinger equation”, Pramana - J Phys, 49:6 (1997), 563
A.A. Andrianov, F. Cannata, J.-P. Dedonder, M.V. Ioffe, “Local realizations of q-oscillators in quantum mechanics”, Physics Letters A, 217:1 (1996), 7
Vyacheslav Spiridonov, “Universal superpositions of coherent states and self-similar potentials”, Phys. Rev. A, 52:3 (1995), 1909
V Spiridonov, A Zhedanov, “Symmetry preserving quantization and self-similar potentials”, J. Phys. A: Math. Gen., 28:22 (1995), L589
A. B. Shabat, “Discrete symmetries and solitons”, Theoret. and Math. Phys., 99:3 (1994), 783–789

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

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Abstract page:	541
Full-text PDF :	225
References:	79
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