Article
Version 1
Preserved in Portico This version is not peer-reviewed
On a Model of Propagation of Two Component Nonlinear OpticalWaves
Version 1
: Received: 24 July 2023 / Approved: 24 July 2023 / Online: 26 July 2023 (08:42:05 CEST)
A peer-reviewed article of this Preprint also exists.
Smirnov, A.O.; Frolov, E.A. On the Propagation Model of Two-Component Nonlinear Optical Waves. Axioms 2023, 12, 983. Smirnov, A.O.; Frolov, E.A. On the Propagation Model of Two-Component Nonlinear Optical Waves. Axioms 2023, 12, 983.
Abstract
Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. Usually, such two-component integrable nonlinear evolutionary equations are considered, the form of which does not depend on the replacement of one component with another. In this paper, we propose for consideration and usage a new hierarchy of two-component integrable nonlinear equations, which have an important difference from the already known equations. Among the hierarchy equations there are analogues of the two-component nonlinear Schrödinger equation (second equation from hierarchy) and the two-component modified Korteweg-de Vries equation (fourth equation from hierarchy). The third equation of the hierarchy is a combination of the nonlinear Schrödinger equation for one component and the modified Korteweg-de Vries equation for the second component. The equations for the individual components are very different from each other, even if they have the same order. Let us note that even hierarchy equations can be reduced to well-known variants of the scalar derivative nonlinear Schrödinger equations, and odd equations can’t be reduced. To construct the hierarchy equations, we use the monodromy matrix method, first proposed by B.A. Dubrovin. Knowledge of the monodromy matrix makes it possible to construct spectral curves of multiphase solutions, as well as to find stationary equations that these solutions satisfy. The last section presents the simplest solutions in the form of solitons and periodic one-phase waves, as well as spectral curves corresponding to these solutions.
Keywords
spectral curve; derivative NLS equation; lax pair; vector NLS equation; monodromy matrix
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
