Absence of sufficiently localized traveling wave solutions for the Novikov-Veselov equation at zero energy
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چکیده
Note also that when E → ±∞, equation (1.1) transforms into another renowned (2 + 1)dimensional analog of KdV, Kadomtsev-Petviashvili equation (KP-I and KP-II, respectively). In addition, a dispersionless analog of (1.1) at E = 0 was derived in [KM] in the framework of a geometrical optics model. Equation (1.1) is contained implicitly in [M] as an equation possessing the following representation ∂(L− E) ∂t = [L− E,A] +B(L− E) (1.4)
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Absence of solitons with sufficient algebraic localization for the Novikov-Veselov equation at nonzero energy
and the corresponding evolution equation (1.1) were given in [NV1], [NV2], where equation (1.1) was also studied in the periodic setting. Solitons and the large time asymptotic behavior of sufficiently localized in space solutions for the Novikov-Veselov equation were studied in the series of works [GN1, G1, Nov2, K1, KN1, KN2, KN3]. In [KN1, K1] it was shown that in the regular case, i.e. when...
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تاریخ انتشار 2012