The Darboux Transformation and <i>N</i>-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space Scale
The coupled cubic-quintic nonlinear Schrödinger (CQNLS) equation is a universal mathematical model describing many physical situations, such as nonlinear optics and Bose–Einstein condensate. In this paper, in order to simplify the process of similar analysis with different forms of the coupled CQNLS...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-12-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/1/12 |
| _version_ | 1827665374033739776 |
|---|---|
| author | Huanhe Dong Chunming Wei Yong Zhang Mingshuo Liu Yong Fang |
| author_facet | Huanhe Dong Chunming Wei Yong Zhang Mingshuo Liu Yong Fang |
| author_sort | Huanhe Dong |
| collection | DOAJ |
| description | The coupled cubic-quintic nonlinear Schrödinger (CQNLS) equation is a universal mathematical model describing many physical situations, such as nonlinear optics and Bose–Einstein condensate. In this paper, in order to simplify the process of similar analysis with different forms of the coupled CQNLS equation, this dynamic system is extended to a time-space scale based on the Lax pair and zero curvature equation. Furthermore, Darboux transformation of the coupled CQNLS dynamic system on a time-space scale is constructed, and the <i>N</i>-soliton solution is obtained. These results effectively combine the theory of differential equations with difference equations and become a bridge connecting continuous and discrete analysis. |
| first_indexed | 2024-03-10T01:27:22Z |
| format | Article |
| id | doaj.art-01d82c0e4264418baa93baabd9d1d339 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T01:27:22Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-01d82c0e4264418baa93baabd9d1d3392023-11-23T13:48:36ZengMDPI AGFractal and Fractional2504-31102021-12-01611210.3390/fractalfract6010012The Darboux Transformation and <i>N</i>-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space ScaleHuanhe Dong0Chunming Wei1Yong Zhang2Mingshuo Liu3Yong Fang4College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaThe coupled cubic-quintic nonlinear Schrödinger (CQNLS) equation is a universal mathematical model describing many physical situations, such as nonlinear optics and Bose–Einstein condensate. In this paper, in order to simplify the process of similar analysis with different forms of the coupled CQNLS equation, this dynamic system is extended to a time-space scale based on the Lax pair and zero curvature equation. Furthermore, Darboux transformation of the coupled CQNLS dynamic system on a time-space scale is constructed, and the <i>N</i>-soliton solution is obtained. These results effectively combine the theory of differential equations with difference equations and become a bridge connecting continuous and discrete analysis.https://www.mdpi.com/2504-3110/6/1/12coupled cubic-quintic nonlinear Schrödinger equationtime-space scalesDarboux transformationN-soliton solution |
| spellingShingle | Huanhe Dong Chunming Wei Yong Zhang Mingshuo Liu Yong Fang The Darboux Transformation and <i>N</i>-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space Scale Fractal and Fractional coupled cubic-quintic nonlinear Schrödinger equation time-space scales Darboux transformation N-soliton solution |
| title | The Darboux Transformation and <i>N</i>-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space Scale |
| title_full | The Darboux Transformation and <i>N</i>-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space Scale |
| title_fullStr | The Darboux Transformation and <i>N</i>-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space Scale |
| title_full_unstemmed | The Darboux Transformation and <i>N</i>-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space Scale |
| title_short | The Darboux Transformation and <i>N</i>-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrödinger Equation on a Time-Space Scale |
| title_sort | darboux transformation and i n i soliton solutions of coupled cubic quintic nonlinear schrodinger equation on a time space scale |
| topic | coupled cubic-quintic nonlinear Schrödinger equation time-space scales Darboux transformation N-soliton solution |
| url | https://www.mdpi.com/2504-3110/6/1/12 |
| work_keys_str_mv | AT huanhedong thedarbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT chunmingwei thedarbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT yongzhang thedarbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT mingshuoliu thedarbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT yongfang thedarbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT huanhedong darbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT chunmingwei darbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT yongzhang darbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT mingshuoliu darbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale AT yongfang darbouxtransformationandinisolitonsolutionsofcoupledcubicquinticnonlinearschrodingerequationonatimespacescale |