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Uspekhi Mat. Nauk, 1994, Volume 49, Issue 6(300), Pages 7–78 (Mi umn1247)  

This article is cited in 23 scientific papers (total in 24 papers)

Huygens' principle and integrability

Yu. Yu. Beresta, A. P. Veselovb

a Moscow Institute of Physics and Technology
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full text: PDF file (3414 kB)
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English version:
Russian Mathematical Surveys, 1994, 49:6, 5–77

Bibliographic databases:

UDC: 517.944
MSC: 35J05, 34M55
Received: 26.10.1994

Citation: Yu. Yu. Berest, A. P. Veselov, “Huygens' principle and integrability”, Uspekhi Mat. Nauk, 49:6(300) (1994), 7–78; Russian Math. Surveys, 49:6 (1994), 5–77

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Berest, YY, “Huygens' principle in Minkowski spaces and soliton solutions of the Korteweg-de Vries equation”, Communications in Mathematical Physics, 190:1 (1997), 113  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Yu. Yu. Berest, A. P. Veselov, “On the singularities of potentials of exactly soluble Schrödinger equations and on Hadamard's problem”, Russian Math. Surveys, 53:1 (1998), 208–209  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Berest, Y, “Hierarchies of Huygens' operators and Hadamard's conjecture”, Acta Applicandae Mathematicae, 53:2 (1998), 125  crossref  mathscinet  zmath  isi  elib
    4. Berest, Y, “D-modules and Darboux transformations”, Letters in Mathematical Physics, 43:3 (1998), 279  crossref  mathscinet  zmath  isi
    5. Pierre C. Sabatier, “Past and future of inverse problems”, J Math Phys (N Y ), 41:6 (2000), 4082  crossref  mathscinet  zmath  isi
    6. S. P. Khekalo, “Fundamental solution for an iterated operator of Cayley–Garding type”, Russian Math. Surveys, 55:3 (2000), 583–585  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Berest, Y, “The problem of lacunas and analysis on root systems”, Transactions of the American Mathematical Society, 352:8 (2000), 3743  crossref  mathscinet  zmath  isi
    8. Plamen Iliev, “q-KP hierarchy, bispectrality and Calogero–Moser systems”, Journal of Geometry and Physics, 35:2-3 (2000), 157  crossref
    9. S. P. Khekalo, “Iso-Huygens Deformations of Homogeneous Differential Operators Related to a Special Cone of Rank 3”, Math. Notes, 70:6 (2001), 847–859  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Fabio A C C Chalub, Jorge P Zubelli, “On Huygens’ Principle for Dirac Operators and Nonlinear Evolution Equations”, Journal of Nonlinear Mathematical Physics, 8:sup1 (2001), 62  crossref
    11. S. P. Khekalo, “Iso-Huygens deformations of the Cayley operator by the general Lagnese–Stellmacher potential”, Izv. Math., 67:4 (2003), 815–836  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Grunbaum, FA, “A noncommutative version of the bispectral problem”, Journal of Computational and Applied Mathematics, 161:1 (2003), 99  crossref  mathscinet  adsnasa  isi  elib
    13. S. P. Khekalo, “The gauge related deformations of the ordinary linear differential operators with constant coefficients”, J. Math. Sci. (N. Y.), 132:1 (2006), 136–145  mathnet  crossref  mathscinet  zmath  elib  elib
    14. S. P. Khekalo, “The Cayley–Laplace differential operator on the space of rectangular matrices”, Izv. Math., 69:1 (2005), 191–219  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    15. S. P. Khekalo, “Stepwise Gauge Equivalence of Differential Operators”, Math. Notes, 77:6 (2005), 843–854  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. S. P. Khekalo, “Temporary deformations of degrees of the wave operator”, J. Math. Sci. (N. Y.), 138:2 (2006), 5603–5612  mathnet  crossref  mathscinet  zmath  elib
    17. S BENSAID, B ORSTED, “The wave equation for Dunkl operators”, Indagationes Mathematicae, 16:3-4 (2005), 351  crossref  elib
    18. Wenjie Wan, Shu Jia, Jason W. Fleischer, “Dispersive superfluid-like shock waves in nonlinear optics”, Nat Phys, 3:1 (2007), 46  crossref  isi
    19. S. P. Khekalo, “Solution of the Hadamard problem in the class of stepwise gauge-equivalent deformations of homogeneous differential operators with constant coefficients”, St. Petersburg Math. J., 19:6 (2008), 1015–1028  mathnet  crossref  mathscinet  zmath  isi  elib
    20. Yuri Berest, Tim Cramer, Farkhod Eshmatov, “Heat Kernel Coefficients for Two-Dimensional Schrödinger Operators”, Comm Math Phys, 283:3 (2008), 853  crossref  mathscinet  zmath  isi  elib
    21. Feigin M., Johnston D., “A Class of Baker-Akhiezer Arrangements”, Commun. Math. Phys., 328:3 (2014), 1117–1157  crossref  isi
    22. V. E. Adler, Yu. Yu. Berest, V. M. Buchstaber, P. G. Grinevich, B. A. Dubrovin, I. M. Krichever, S. P. Novikov, A. N. Sergeev, M. V. Feigin, J. Felder, E. V. Ferapontov, O. A. Chalykh, P. I. Etingof, “Alexander Petrovich Veselov (on his 60th birthday)”, Russian Math. Surveys, 71:6 (2016), 1159–1176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. S. P. Khekalo, “Dunkl–Darboux differential-difference operators”, Izv. Math., 81:1 (2017), 156–178  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    24. V. V. Meshcheryakov, “Burchnall–Chaundy Polynomials and Dunkl–Darboux Operators”, Math. Notes, 102:2 (2017), 261–267  mathnet  crossref  crossref  mathscinet  isi  elib
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