zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Quasi-periodic solutions of the $2+1$ dimensional modified Korteweg-de Vries equation. (English) Zbl 0937.35155
Summary: A new $2 + 1$ dimensional modified Korteweg-de Vries equation is proposed and decomposed into the first two members of the well-known Kaup-Newell hierarchy, which are reduced further into integrable ordinary differential equations in the invariant set produced by the stationary Kaup-Newell equation. The Abel-Jacobi coordinates are introduced to straighten out the flows, from which quasi-periodic solutions of the $2 + 1$ dimensional modified Korteweg-de Vries equation are obtained in terms of the Riemann theta functions.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35B10Periodic solutions of PDE
37K20Relations of infinite-dimensional systems with algebraic geometry, etc.
WorldCat.org
Full Text: DOI
References:
[1] C.W. Cao, X.G. Geng, in: C.H. Gu, Y.S. Li, G.Z. Tu (Eds.), Nonlinear Physics, Research Reports in Physics, Springer, Berlin, 1990, pp. 68--78.
[2] Cao, C. W.: Sci. China A. 33, 528 (1990)
[3] Cao, C. W.; Geng, X. G.: J. phys. A: math. Gen.. 23, 4117 (1990)
[4] Antonowicz, M.; Rauch-Wojciechowski, S.: J. phys. A: math. Gen.. 24, 5043 (1991)
[5] Antonowicz, M.; Rauch-Wojciechowski, S.: J. math. Phys.. 33, 2115 (1992)
[6] Konopelchenko, B.; Dubrovsky, V.: Phys. lett.. 102A, 45 (1984)
[7] Konopelchenko, B.; Strampp, W.: Phys. lett. A. 157, 17 (1991)
[8] Konopelchenko, B.; Strampp, W.: J. phys. A: math. Gen.. 25, 4399 (1992)
[9] Cheng, Y.; Li, Y. S.: Phys. lett. A. 157, 22 (1991)
[10] Cheng, Y.; Li, Y. S.: J. phys. A: math. Gen.. 25, 419 (1992)
[11] Kaup, D. J.; Newell, A. C.: J. math. Phys.. 19, 799 (1978)
[12] C.L. Siegel, Topics in Complex Function Theory, vol. 2, Wiley, New York, 1971. · Zbl 0211.10501
[13] P. Griffiths, J. Harris, Principles of Algebraic Geometry, Wiley, New York, 1994. · Zbl 0836.14001
[14] S. Novikov, S.V. Manakov, L.P. Pitaevskii, V.E. Zakharov, Theory of Solitons, The Inverse Scattering Methods, Consultants Bureau, New York, 1984. · Zbl 0598.35002
[15] A.C. Newell, Solitons in Mathematics and Physics, SIAM, Philadelphia, 1985. · Zbl 0565.35003
[16] Date, E.: Prog. theor. Phys.. 59, 265 (1978)
[17] Tracy, E. R.; Chen, H. H.; Lee, Y. C.: Phys. rev. Lett.. 53, 218 (1984)