Completion of the integrable coupling systems

Yao, Yuqin; Li, Chunxia; Shen, Shenfeng

doi:10.48550/arxiv.1711.04073

Cited by 1 publication

(1 citation statement)

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“…The super Hamiltonian structure of a super NLS-mKdV hierarchy is obtained by using super trace identity [26]. To further study NLS-mKdV hierarchy, researchers construct the completion of the NLS-mKdV integrable coupling systems and binary nonlinearization [18,24]. There are many methods to obtain explicit solutions of integrable equations, for instance, Darboux transformation method [4,14,23], inverse scattering transformation [1,2], Hirota method [7,21], Bäcklund transformation [16,9], and so on.…”

Section: Introductionmentioning

confidence: 99%

Integrable nonlinear perturbed hierarchies of NLS-mKdV equation and soliton solutions

Zhao¹,

Cheng²,

Li³

et al. 2022

ejde

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We propose three spectral problems for NLS-mKdV equation by combining three integrable coupling ways. Then we obtain three nonlinear perturbation terms to derive three integrable nonlinear perturbed hierarchies of the NLS-mKdV equation. We proved the Lax integrability of the integrable nonlinear perturbed hierarchies. On the basis of a special orthogonal group, we prove the Liouville integrability of a third-order integrable nonlinear perturbed hierarchy of NLS-mKdV equation by deriving its bi-Hamiltonian structures. We build three Darboux matrices for constructing the Darboux transformations of the first two equations. As applications of the Darboux transformation, we present explicit solutions of these equations, three-dimensional plots, and density profiles the evolution of solitary waves.

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