Abstract:§ 0. IntroductionIn his lectures at Kyoto University, Professor M. Sato presented a program for generalizing the soliton theory ([9] ; cf. [10]). The KadomtsevPetviashvili (KP) equation is a typical example of the soliton theory. The KP equation is written in the form of deformation equations of a linear ordinary differential equation. The time evolutions of a solution are interpreted as dynamical motions on an infinite dimensional Grassmann manifold ([7], [9]). The Lie algebra of microdifferential operators… Show more
“…Lemma 3.2 (see [9]). Fix an operator P E g. Let a family of D-submodules It satisfy both (3.5) and (3.7) for any t. Then (3.7) reduces to the equation…”
Section: P(d) = Hd + [Wlh] + O(d'~l)mentioning
confidence: 99%
“…In this section we return to the commutative (in the DGA-sense) de Rham complex and describe (following [9]) the Sato equations for deformations of D-modules in some specific example.…”
Section: ~[ D]= =0 W 3 the Sato Equations For The Deformations Of Dmentioning
confidence: 99%
“…Let us write the equations of motion with respect to the time variables tp and tQ generated by P and Q, (see [9]). The compatibility condition for system (3.9), (3.9') is…”
Section: Ow(t) = -(Wpw-a)-wmentioning
confidence: 99%
“…The family of subspaces {E(ra)} m 6 Z defines an increasing filtration of E such that for any ra, n 6 Z Lemma 3.1 (see [9]). Let a D-submodule I satisfy (3.5).…”
Section: This Can Easily Be Explained By Means Of the Formal Laplace mentioning
confidence: 99%
“…In w we describe, following [9], the Sato equations for the deformations of D-modules in a certain specific example.…”
“…Lemma 3.2 (see [9]). Fix an operator P E g. Let a family of D-submodules It satisfy both (3.5) and (3.7) for any t. Then (3.7) reduces to the equation…”
Section: P(d) = Hd + [Wlh] + O(d'~l)mentioning
confidence: 99%
“…In this section we return to the commutative (in the DGA-sense) de Rham complex and describe (following [9]) the Sato equations for deformations of D-modules in some specific example.…”
Section: ~[ D]= =0 W 3 the Sato Equations For The Deformations Of Dmentioning
confidence: 99%
“…Let us write the equations of motion with respect to the time variables tp and tQ generated by P and Q, (see [9]). The compatibility condition for system (3.9), (3.9') is…”
Section: Ow(t) = -(Wpw-a)-wmentioning
confidence: 99%
“…The family of subspaces {E(ra)} m 6 Z defines an increasing filtration of E such that for any ra, n 6 Z Lemma 3.1 (see [9]). Let a D-submodule I satisfy (3.5).…”
Section: This Can Easily Be Explained By Means Of the Formal Laplace mentioning
confidence: 99%
“…In w we describe, following [9], the Sato equations for the deformations of D-modules in a certain specific example.…”
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