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Zh. Mat. Fiz. Anal. Geom., 2008, Volume 4, Number 4, Pages 490–528 (Mi jmag110)  

This article is cited in 13 scientific papers (total in 13 papers)

Kdv flow on generalized reflectionless potentials

S. Kotani

Kwansei Gakuen University School of Science and Technology Hyogo, 2-1 Gakuen, Sanda-shi, Hyogo 669-1337, Japan

Abstract: The purpose of this article is to construct KdV flow on a space of generalized reflectionless potentials by applying Sato's Grassmannian approach. The point is that the base space contains not only rapidly decreasing potentials but also oscillating ones such as periodic ones, which makes it possible for us to discuss the shift invariant probability measures on it.

Key words and phrases: Korteweg de Vries equation, inverse spectral methods, reflectionless potentials.

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Bibliographic databases:
MSC: 35Q53, 37K15
Received: 14.04.2008

Citation: S. Kotani, “Kdv flow on generalized reflectionless potentials”, Zh. Mat. Fiz. Anal. Geom., 4:4 (2008), 490–528

Citation in format AMSBIB
\by S.~Kotani
\paper Kdv flow on generalized reflectionless potentials
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2008
\vol 4
\issue 4
\pages 490--528

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    This publication is cited in the following articles:
    1. Johnson R., Zampogni L., “Remarks of a paper of Kotani concerning generalized reflectionless Schrödinger potentials”, Discrete Contin. Dyn. Syst.-Ser. B, 14:2 (2010), 559–586  crossref  mathscinet  zmath  isi  elib
    2. Johnson R., Zampogni L., “On the Camassa-Holm and K-dV hierarchies”, J. Dynam. Differential Equations, 22:2 (2010), 331–366  crossref  mathscinet  zmath  isi  elib
    3. El G.A., Kamchatnov A.M., Pavlov M.V., Zykov S.A., “Kinetic equation for a soliton gas and its hydrodynamic reductions”, J. Nonlinear Sci., 21:2 (2011), 151–191  crossref  mathscinet  zmath  isi  elib
    4. Johnson R., Zampogni L., “The Sturm-Liouville Hierarchy of Evolution Equations II”, Adv. Nonlinear Stud., 12:3 (2012), 501–532  crossref  zmath  isi
    5. Aihara H., Akahori J., Fujii H., Nitta Ya., “Tau Functions of Kp Solitons Realized in Wiener Space”, Bull. London Math. Soc., 45:6 (2013), 1301–1309  crossref  zmath  isi  scopus
    6. Volberg A., Yuditskii P., “Kotani-Last Problem and Hardy Spaces on Surfaces of Widom Type”, Invent. Math., 197:3 (2014), 683–740  crossref  mathscinet  zmath  isi  elib
    7. Damanik D., Yuditskii P., “Counterexamples To the Kotani-Last Conjecture For Continuum Schrodinger Operators Via Character-Automorphic Hardy Spaces”, Adv. Math., 293 (2016), 738–781  crossref  mathscinet  zmath  isi  elib
    8. El G.A., “Critical Density of a Soliton Gas”, Chaos, 26:2 (2016), 023105  crossref  mathscinet  isi
    9. Johnson R., Zampogni L., “Remarks on the Generalized Reflectionless Schrodinger Potentials”, J. Dyn. Differ. Equ., 28:3-4, SI (2016), 925–953  crossref  zmath  isi  scopus
    10. Johnson R., Zampogni L., “Some Examples of Generalized Reflectionless Schrodinger Potentials”, Discret. Contin. Dyn. Syst.-Ser. S, 9:4 (2016), 1149–1170  crossref  zmath  isi  scopus
    11. Hur I., McBride M., Remling Ch., “The Marchenko Representation of Reflectionless Jacobi and Schrodinger Operators”, Trans. Am. Math. Soc., 368:2 (2016), PII S 0002-9947(2015)06527-1, 1251–1270  crossref  zmath  isi
    12. Damanik D., Goldstein M., Lukic M., “The Isospectral Torus of Quasi-Periodic Schrodinger Operators Via Periodic Approximations”, Invent. Math., 207:2 (2017), 895–980  crossref  mathscinet  zmath  isi  scopus
    13. S. Kotani, “Construction of KdV flow I. $\tau$-Function via Weyl function”, Zhurn. matem. fiz., anal., geom., 14:3 (2018), 297–335  mathnet  crossref
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