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An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects. (English. Russian original) Zbl 1362.37141

Theor. Math. Phys. 189, No. 1, 1450-1458 (2016); translation from Teor. Mat. Fiz. 189, No. 1, 59-68 (2016).
The authors consider the Pavlov equation \( v_{xt}+ v_{yy} + v_x v_{xy} - v_y v_{xx}=0 \). This equation can be written as commutativity condition of two vector fields. This representation is used to solve the Pavlov equation via inverse scattering transform. In the present paper, the authors use Radon transform and integral geometry to add some new insight to a result obtained in [the authors, Stud. Appl. Math. 137, No. 1, 10–27 (2016; Zbl 1344.35126)].

MSC:

37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
44A12 Radon transform

Citations:

Zbl 1344.35126
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References:

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