Xuehui Zhao | Searcharxiv

arXiv2026

Nonlinearization of bilinear equations of the sine-Gordon type, nonlinear Schr\"odinger type and Benjamin-Ono type

This is a continuation of the paper [Commun. Theor. Phys., 77 (2025) 115006] on the nonlinearization of bilinear equations. The sine-Gordon type and nonlinear Schr\"odinger type bilinear equations are introduced by Jarmo Hietarinta during his search for integrable bilinear equations. In this paper, we provide a formulation to convert these two types of bilinear equations into nonlinear forms. In addition, the nonlinearization related to the equations involving the Hilbert transformations is also considered. Bell polynomials are employed in the nonlinearization and illustrative examples are provided.

nlin.SI↗

arXiv2023

Symmetries of the D$Δ$mKP hierarchy and their continuum limits

In the recent paper [Stud. App. Math. 147 (2021) 752], squared eigenfunction symmetry constraint of the differential-difference modified Kadomtsev-Petviashvili (D$Δ$mKP) hierarchy converts the D$Δ$mKP system to the relativistic Toda spectral problem and its hierarchy. In this paper we introduce a new formulation of independent variables in the squared eigenfunction symmetry constraint, under which the D$Δ$mKP system gives rise to the discrete spectral problem and a hierarchy of the differential-difference derivative nonlinear Schrödinger equation of the Chen-Lee-Liu type. In addition, by introducing nonisospectral flows, two sets of symmetries of the D$Δ$mKP hierarchy and their algebraic structure are obtained. We then present a unified continuum limit scheme, by which we achieve the correspondence of the mKP and the D$Δ$mKP hierarchies and their integrable structures.

nlin.SI↗