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On the Indication from Pioneer 10/11 Data of an Anomalous Acceleration
Hubble's law, which states a linear increase in velocities with distances,
can physically be understood in terms of an acceleration cH. This work proposes
a connection between this "universal" acceleration seen in the solar system and
the anomalous acceleration acting on the Pioneer 10/11 spacecraft, in which the
Hubble constant inferred from Pioneer 10/11 data is ~ 87 km/s/Mpc. Its physical
implication is discussed in relation with Mach's principle.Comment: Written originally in two part
The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions
In this paper we apply the formal Inverse Spectral Transform for integrable
dispersionless PDEs arising from the commutation condition of pairs of
one-parameter families of vector fields, recently developed by S. V. Manakov
and one of the authors, to one distinguished class of equations, the so-called
Dunajski hierarchy. We concentrate, for concreteness, i) on the system of PDEs
characterizing a general anti-self-dual conformal structure in neutral
signature, ii) on its first commuting flow, and iii) on some of their basic and
novel reductions. We formally solve their Cauchy problem and we use it to
construct the longtime behavior of solutions, showing, in particular, that
unlike the case of soliton PDEs, different dispersionless PDEs belonging to the
same hierarchy of commuting flows evolve in time in very different ways,
exhibiting either a smooth dynamics or a gradient catastrophe at finite time
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