Integrable nonlinear perturbed hierarchies of NLS-mKdV equation and soliton solutions
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Date
2022-10-13
Authors
Zhao, Qiulan
Cheng, Hongbiao
Li, Xinyue
Li, Chuanzhong
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Integrable perturbed hierarchies, Nonlinear perturbation terms, Darboux transformation, Soliton solutions
Citation
Zhao, Q., Cheng, H., Li, X., & Li, C. (2022). Integrable nonlinear perturbed hierarchies of NLS-mKdV equation and soliton solutions. <i>Electronic Journal of Differential Equations, 2022</i>(71), pp. 1-32.
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Attribution 4.0 International