Geodesic
Coupled Modified KP Hierarchy and Its Dispersionless Limit
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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We define the coupled modified KP hierarchy and its dispersionless limit. This integrable hierarchy is a generalization of the “half” of the Toda lattice hierarchy as well as an extension of the mKP hierarchy. The solutions are parametrized by a fibered flag manifold. The dispersionless counterpart interpolates several versions of dispersionless mKP hierarchy.
Keywords: cmKP hierarchy; fibered flag manifold; dcmKP hierarchy. 
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     author = {Takashi Takebe and Lee-Peng Teo},
     title = {Coupled {Modified} {KP} {Hierarchy} and {Its} {Dispersionless} {Limit}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2006},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a71/}
}
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Takashi Takebe; Lee-Peng Teo. Coupled Modified KP Hierarchy and Its Dispersionless Limit. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a71/

[1] Chang J. H., Tu M. H., “On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies”, J. Math. Phys., 41 (2000), 5391–5406 ; solv-int/9912016 | DOI | MR | Zbl

[2] Dickey L. A., “Modified KP and discrete KP”, Lett. Math. Phys., 48 (1999), 277–289 ; solv-int/9902008 | DOI | MR | Zbl

[3] Date E., Kashiwara M., Jimbo M., Miwa T., “Transformation groups for soliton equations”, Nonlinear Integrable Systems – Classical Theory and Quantum Theory, World Scientific, Singapore, 1983, 39–119 | MR

[4] Duren P. L., Univalent functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer-Verlag, New York, 1983 | MR | Zbl

[5] Kashiwara M., Miwa T., “Transformation groups for soliton equations. I. The $\tau$ function of the Kadomtsev–Petviashvili equation”, Proc. Japan Acad. Ser. A Math. Sci., 57 (1981), 342–347 | DOI | MR | Zbl

[6] Kac V. G., Peterson D. H., “Lectures on the infinite wedge-representation and the MKP hierarchy”, Systèmes dynamiques non linéaires: intégrabilité et comportement qualitatif, Sém. Math. Sup., 102, Presses Univ. Montréal, Montreal, 1986, 141–184 | MR

[7] Kupershmidt B. A., KP or mKP. Noncommutative mathematics of Lagrangian, Hamiltonian, and integrable systems, Mathematical Surveys and Monographs, 78, American Mathematical Society, Providence, RI, 2000 | MR | Zbl

[8] Kupershmidt B. A., “The quasiclassical limit of the modified KP hierarchy”, J. Phys. A: Math. Gen., 23 (1990), 871–886 | DOI | MR | Zbl

[9] Pommerenke C., Univalent functions, Studia Mathematica/Mathematische Lehrbücher, 25, Vandenhoeck Ruprecht, Göttingen, 1975, with a chapter on quadratic differentials by Gerd Jensen | MR

[10] Sato M., “Soliton equations as dynamical systems on an infinite dimensional Grassmann manifold”, RIMS Kokyuroku, 439 (1981), 30–46 | Zbl

[11] Sato M., Noumi M., Soliton equations and the universal Grassmann manifolds, Sophia University Kokyuroku in Math., 18, Sophia University, Tokyo, 1984 (in Japanese) | Zbl

[12] Sato M., Sato Y., “Soliton equations as dynamical systems on infinite dimensional Grassmann manifold”, Nonlinear Partial Differential Equations in Applied Science, Proceedings of the U.S.–Japan Seminar (1982, Tokyo), Lect. Notes in Num. Anal., 5, 1982, 259–271 | MR

[13] Takasaki K., “Initial value problem for the Toda lattice hierarchy”, Group Representations and Systems of Differential Equations (1982, Tokyo), Adv. Stud. Pure Math., 4, North-Holland, Amsterdam, 1984, 139–163 | MR

[14] Takebe T., “Toda lattice hierarchy and conservation laws”, Comm. Math. Phys., 129 (1990), 281–318 | DOI | MR | Zbl

[15] Takebe T., “Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy. I”, Lett. Math. Phys., 21 (1991), 77–84 | DOI | MR | Zbl

[16] Takebe T., “Representation theoretical meaning of the initial value problem for the Toda lattice hierarchy. II”, Publ. RIMS, 27 (1991), 491–503 | DOI | MR | Zbl

[17] Takebe T., “A note on modified KP hierarchy and its (yet another) dispersionless limit”, Lett. Math. Phys., 59 (2002), 157–172 ; nlin.SI/0111012 | DOI | MR | Zbl

[18] Teo L.-P., On dispersionless coupled modified KP hierarchy, nlin.SI/0304007

[19] Teo L.-P., “Analytic functions and integrable hierarchies – characterization of tau functions”, Lett. Math. Phys., 64 (2003), 75–92 ; hep-th/0305005 | DOI | MR | Zbl

[20] Takasaki K., Takebe T., “$\rm SDiff(2)$ KP hierarchy”, Infinite Analysis, Part A, B (1991, Kyoto), Adv. Ser. Math. Phys., 16, World Sci. Publishing, River Edge, NJ, 1992, 889–922 ; hep-th/9112046 | MR

[21] Takasaki K., Takebe T., “Integrable hierarchies and dispersionless limit”, Rev. Math. Phys., 7 (1995), 743–808 ; hep-th/9405096 | DOI | MR | Zbl

[22] Takasaki K., Takebe T., “Löwner equations and dispersionless hierarchies”, the Proceedings of XXIII International Conference of Differential Geometric Methods in Theoretical Physics (August 2005, Tianjin, China), Nankai Institute of Mathematics, 10, World Scientific, Hackensack, NJ, 2006, 438–442 ; nlin.SI/0512008 | MR | Zbl

[23] Ueno K., Takasaki K., “Toda lattice hierarchy”, Group Representations and Systems of Differential Equations (1982, Tokyo), Adv. Stud. Pure Math., 4, North-Holland, Amsterdam, 1984, 1–95 | MR