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Sung, Li-yeng

doi:10.1023/a:1009806923447

Cited by 9 publications

(2 citation statements)

References 12 publications

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“…In our case, since we work in T x × R y rather than in T × T, the mean value has to satisfy the zero mass constraint (1.4), otherwise we do not have decay to zero as |y| → ∞. For more about the zero mass constraint see also [15,30,35].…”

Section: Introductionmentioning

confidence: 99%

A semi-periodic initial-value problem for the Kadomtsev–Petviashvili II equation

Kalamvokas,

Papageorgiou,

Fokas

et al. 2023

Nonlinearity

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We investigate the Cauchy problem on the cylinder, namely the semi-periodic problem where there is periodicity in the x-direction and decay in the y-direction, for the Kadomtsev–Petviashvili II equation by the inverse spectral transform method. For initial data with small L 1 and L 2 norms, assuming the zero mass constraint, this initial-value problem is reduced to a Riemann–Hilbert problem on the boundary of certain infinite strips with shift.

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Section: Introductionmentioning

confidence: 99%

A semi-periodic initial-value problem for the Kadomtsev–Petviashvili II equation

Kalamvokas,

Papageorgiou,

Fokas

et al. 2023

Nonlinearity

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“…In [62], precise asymptotics are given for KP-II in the case of small data with eight derivatives in L 1 ∩ L 2 . In the KP-I case, a similar description is established for the case of small data in the Schwartz class [59]. See [23,24] for a complete description of the state of art via the use of rigorous ISTs.…”

Section: Theorem 11 (Central Decay)mentioning

confidence: 96%

Long time asymptotics of large data in the Kadomtsev–Petviashvili models

Mendez,

Muñoz,

Poblete

et al. 2024

Nonlinearity

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We consider the Kadomtsev–Petviashvili (KP) equations posed on R 2 . For both models, we provide sequential in time asymptotic descriptions of solutions obtained from arbitrarily large initial data, inside regions of the plane not containing lumps or line solitons, and under minimal regularity assumptions. The proof involves the introduction of two new virial identities adapted to the KP dynamics. This new approach is particularly important in the KP-I case, where no monotonicity property was previously known. The core of our results do not require the use of the integrability of KP and are adaptable to well-posed perturbations.

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