منابع مشابه
An Improved Local Wellposedness Result for the Modified Kdv-equation
The Cauchy problem for the modified KdV-equation ut + uxxx = (u 3)x, u(0) = u0 is shown to be locally wellposed for data u0 in the space Ĥr s (R) defined by the norm ‖u0‖ Ĥr s := ‖〈ξ〉sû0‖Lr′ ξ , provided 4 3 < r ≤ 2, s ≥ 1 2 − 1 2r . For r = 2 this coincides with the best possible result on the H-scale due to Kenig, Ponce and Vega. The proof uses an appropriate variant of the Fourier restrictio...
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In [28] Rasin and Hydon suggested a way to construct an infinite number of conservation laws for the discrete KdV equation (dKdV), by repeated application of a certain symmetry to a known conservation law. It was not decided, however, whether the resulting conservation laws were distinct and nontrivial. In this paper we obtain the following results: (1) We give an alternative method to construc...
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We prove the conjectural relationship recently proposed in [16] between certain special cubic Hodge integrals of the Gopakumar–Mariño–Vafa type [27, 36] and GUE correlators.
متن کاملRogue periodic waves of the modified KdV equation
Rogue periodic waves stand for rogue waves on the periodic background. Two families of traveling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions to the mKdV equation. Since t...
متن کاملQuantum lattice KdV equation
A quantum theory is developed for a difference-difference system which can serve as a toy-model of the quantum Korteveg-de-Vries equation. Introduction This Letter presents an example of a completely integrable ‘discrete-space-time quantum model’ whose Heisenberg equations of motion have the form φ (τ, n) φ (τ, n− 1) + λ φ (τ, n− 1) φ (τ − 1, n− 1) = λ φ (τ, n) φ (τ − 1, n) + φ (τ − 1, n) φ (τ ...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1992
ISSN: 0033-068X
DOI: 10.1143/ptp.88.1033