Fokas-Lenells Derivative nonlinear Schrödinger equation its associated soliton surfaces and Gaussian curvature
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911905608630272 |
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| author | Talukdar, Sagardeep Dutta, Riki Saharia, Gautam Kumar Nandy, Sudipta |
| author_facet | Talukdar, Sagardeep Dutta, Riki Saharia, Gautam Kumar Nandy, Sudipta |
| contents | One of the most important tasks in mathematics and physics is to connect differential geometry and nonlinear differential equations. In the study of nonlinear optics, integrable nonlinear differential equations such as the nonlinear Schrödinger equation (NLSE) and higher-order NLSE (HNLSE) play crucial roles. Because of the medium's balance between dispersion and nonlinearity, all of these systems display soliton solutions. The soliton surfaces, or manifolds, connected to these integrable systems hold significance in numerous areas of mathematics and physics. We examine the use of soliton theory in differential geometry in this paper. We build the two-dimensional soliton surface in the three-dimensional Euclidean space by taking into account the Fokas-Lenells Derivative nonlinear Schrödinger equation (also known as the gauged Fokas-Lenells equation). The same is constructed by us using the Sym-Tafel formula. The first and second fundamental forms, surface area, and Gaussian curvature are obtained using a Lax representation of the gauged FLE. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_03203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fokas-Lenells Derivative nonlinear Schrödinger equation its associated soliton surfaces and Gaussian curvature Talukdar, Sagardeep Dutta, Riki Saharia, Gautam Kumar Nandy, Sudipta Exactly Solvable and Integrable Systems One of the most important tasks in mathematics and physics is to connect differential geometry and nonlinear differential equations. In the study of nonlinear optics, integrable nonlinear differential equations such as the nonlinear Schrödinger equation (NLSE) and higher-order NLSE (HNLSE) play crucial roles. Because of the medium's balance between dispersion and nonlinearity, all of these systems display soliton solutions. The soliton surfaces, or manifolds, connected to these integrable systems hold significance in numerous areas of mathematics and physics. We examine the use of soliton theory in differential geometry in this paper. We build the two-dimensional soliton surface in the three-dimensional Euclidean space by taking into account the Fokas-Lenells Derivative nonlinear Schrödinger equation (also known as the gauged Fokas-Lenells equation). The same is constructed by us using the Sym-Tafel formula. The first and second fundamental forms, surface area, and Gaussian curvature are obtained using a Lax representation of the gauged FLE. |
| title | Fokas-Lenells Derivative nonlinear Schrödinger equation its associated soliton surfaces and Gaussian curvature |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2406.03203 |