Hermite–Padé approximations with Pfaffian structures: Novikov peakon equation and integrable lattices

Chang, Xiang-Ke

doi:10.1016/j.aim.2022.108338

Cited by 5 publications

(1 citation statement)

References 36 publications

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“…Wu et al obtained N -soliton solutions for the Novikov equation through Darboux transformations [10]. Recently, Chang et al applied Pfaffian technique to investigate multipeakons of the Novikov equation, establishing a connection between the Novikov peakons and the finite Toda lattice of BKP type, as well as employing Hermite-Pade approximation to address the Novikov peakon problem [11,12]. Boutet de Monvel et al developed the inverse scattering theory to the Novikov equation (1.1) with a nonzero constant background [13].…”

Section: Introductionmentioning

confidence: 99%

The Defocusing Nonlinear Schrödinger Equation with a Nonzero Background: Painlevé Asymptotics in Two Transition Regions

Wang

Fan

2023

Commun. Math. Phys.

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In the present work, we investigate the long-time asymptotics of the defocusing mKdV equation under a nonzero background. Using the ∂ generalization of the nonlinear steepest descent approach as well as the double scaling limit skill, the long-time asymptotics of the solution in the transition region |x/t + 6|t 2/3 ≤ C is obtained, which is associated to the Hastings-McLeod solution of the Painlevé II (PII) equation in the generic case, while Ablowitz-Segur solution in the non-generic case.

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