Absence of exponentially localized solitons for the Novikov–Veselov equation at negative energy
نویسندگان
چکیده
We show that Novikov–Veselov equation (an analog of KdV in dimension 2 + 1) does not have exponentially localized solitons at negative energy.
منابع مشابه
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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Abstract. In the present paper we are concerned with the Novikov–Veselov equation at negative energy, i.e. with the (2+1)–dimensional analog of the KdV equation integrable by the method of inverse scattering for the two–dimensional Schrödinger equation at negative energy. We show that the solution of the Cauchy problem for this equation with non–singular scattering data behaves asymptotically a...
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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...
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تاریخ انتشار 2011