Nonlocal integrable equations from the mKP hierarchy

Rui, Wenjuan; Cheng, Jipeng

doi:10.1007/s13324-022-00750-1

Cited by 2 publications

(1 citation statement)

References 40 publications

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“…A prominent feature of the sncILW equation is its nonlocality, which arises through integral operators (see (1.4)-(1.5) below). While soliton equations with this feature have been studied for a long time (the classical examples are the Benjamin-Ono [5,6] and intermediate long wave [7,8] equations), there has recently been considerable interest in constructing and analyzing novel nonlocal soliton equations; see, for instance, [9,10,11,12,13,14,15,16]. In this context, in addition to resolving a conjecture posed in [1], this paper serves to exhibit the sncILW equation with periodic boundary conditions as an interesting system worthy of further study.…”

Section: Introductionmentioning

confidence: 99%

On the non-chiral intermediate long wave equation

2022

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We study integrability properties of the non-chiral intermediate long wave equation recently introduced by the authors as a parity-invariant variant of the intermediate long wave equation. For this new equation we: (a) derive a Lax pair, (b) derive a Hirota bilinear form, (c) derive a Bäcklund transformation, (d) use, separately, the Bäcklund transformation and the Lax representation to obtain an infinite number of conservation laws.

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Section: Introductionmentioning

confidence: 99%

On the non-chiral intermediate long wave equation

2022

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Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation

2023

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We construct elliptic multi-soliton solutions of the spin non-chiral intermediate long-wave (sncILW) equation with periodic boundary conditions. These solutions are obtained by a spin-pole ansatz including a dynamical background term; we show that this ansatz solves the periodic sncILW equation provided the spins and poles satisfy the elliptic A-type spin Calogero-Moser (sCM) system with certain constraints on the initial conditions. The key to this result is a Bäcklund transformation for the elliptic sCM system which includes a non-trivial dynamical background term. We also present solutions of the sncILW equation on the real line and of the spin Benjamin–Ono equation which generalize previously obtained solutions by allowing for a non-trivial background term.

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Nonlocal integrable equations from the mKP hierarchy

Cited by 2 publications

References 40 publications

On the non-chiral intermediate long wave equation

On the non-chiral intermediate long wave equation

Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation

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