Work

Derivation and simulation of the multiple lump solutions to an integrable generalized fifth-order Korteweg–de Vries equation

Year: 2026

Type: article

Abstract: In this paper, we develop two methods for constructing lump solutions to the generalized fifth-order Korteweg–de Vries (KdV) equation, including the inverse scattering transform (IST) method and the ∂¯-dressing method. Making use of the IST method, we construct standard M-lump solutions originating from eigenfunctions containing simple poles, while also obtaining non-standard lump solutions corresponding to eigenfunctions with higher-order poles. Moreover, we present both standard three-lump solutions and non-standard four-lump solutions, which have not been reported in previous studies. By applying the Zakharov–Manakov ∂¯-dressing method, we construct two classes of lump solutions for the generalized fifth-order KdV equation with integrable boundary condition uy|y=0, corresponding to kernels with purely imaginary and real spectral points, respectively.

Source: Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

DOI: 10.1098/rspa.2025.0724

Authors: Huan-Huan Lu, Wei-Qi Peng

Institutions: China University of Mining and Technology, Ocean University of China

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: Qingdao Postdoctoral Science Foundation, National Natural Science Foundation of China, Natural Science Foundation of Shandong Province, Fundamental Research Funds for the Central Universities

Awards: G4251934030, G4896793637, G5450259278, G8308030364