2002
DOI: 10.1063/1.1481545
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Dispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical ∂̄-dressing method

Abstract: A note on reductions of the dispersionless Toda hierarchy J. Math. Phys. 51, 122704 (2010) The quasiclassical limit of the scalar nonlocal ‫ץ‬ -problem is derived and a quasiclassical version of the ‫ץ‬ -dressing method is presented. Dispersionless KadomtsevPetviashvili ͑KP͒, modified KP, and dispersionless two-dimensional Toda lattice ͑2DTL͒ hierarchies are discussed as illustrative examples. It is shown that the universal Whitham hierarchy is nothing but the ring of symmetries for the quasiclassical ‫ץ‬ -pro… Show more

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Cited by 47 publications
(81 citation statements)
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“…The quasiclassical∂-dressing scheme for dispersionless KP hierarchy [18,19,20,21] is based on nonlinear Beltrami equation…”
Section: Dkp and Dbkp Hierarchiesmentioning
confidence: 99%
See 2 more Smart Citations
“…The quasiclassical∂-dressing scheme for dispersionless KP hierarchy [18,19,20,21] is based on nonlinear Beltrami equation…”
Section: Dkp and Dbkp Hierarchiesmentioning
confidence: 99%
“…In the dispersionless case the study of hierarchies of B type is just in the very beginning [28,20].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Another example is the more recent version of the KP equation, namely so-called KP of type B (BKP) (see [18,5]). The dispersionless BKP is of the form u t = α u x u 2 + β u y u + u x ∂ −1…”
Section: The Kp and Bkp Equations As Two Generalizations Of Kdvmentioning
confidence: 99%
“…In particular we would like to derive dHirota equations of a universal integrable hierarchy underlying topological Landau-Ginzburg models of D-type proposed by Takasaki [23]. Since this integrable hierarchy is an extension of the dispersionless BKP (dBKP) hierarchy [7,22,15,2] and has two sets of time variables we refer it to the extended dispersionless BKP (EdBKP) hierarchy [6]. The EdBKP hierarchy resembles the dToda hierarchy in many formulations such as dressing operators, Orlov functions, Riemann-Hilbert problem, additional symmetries, w-algebras, hodograph solutions etc.…”
Section: Introductionmentioning
confidence: 99%