Nonlinear mirror image method for nonlinear Schrödinger equation: Absorption/emission of one soliton by a boundary - Université de Tours Accéder directement au contenu
Article Dans Une Revue Stud.Appl.Math. Année : 2022

Nonlinear mirror image method for nonlinear Schrödinger equation: Absorption/emission of one soliton by a boundary

Résumé

We perform the analysis of the focusing nonlinear Schrödinger equation on the half-line with time-dependent boundary conditions along the lines of the nonlinear method of images with the help of Bäcklund transformations. The difficulty arising from having such time-dependent boundary conditions at $x=0$ is overcome by changing the viewpoint of the method and fixing the Bäcklund transformation at infinity as well as relating its value at $x=0$ to a time-dependent reflection matrix. The interplay between the various aspects of integrable boundary conditions is reviewed in detail to brush a picture of the area. We find two possible classes of solutions. One is very similar to the case of Robin boundary conditions whereby solitons are reflected at the boundary, as a result of an effective interaction with their images on the other half-line. The new regime of solutions supports the existence of one soliton that is not reflected at the boundary but can be either absorbed or emitted by it. We demonstrate that this is a unique feature of time-dependent integrable boundary conditions.
Fichier principal
Vignette du fichier
2107.02747.pdf (791.91 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03287289 , version 1 (10-10-2022)

Identifiants

Citer

Vincent Caudrelier, Nicolas Crampe, Carlos Mbala Dibaya. Nonlinear mirror image method for nonlinear Schrödinger equation: Absorption/emission of one soliton by a boundary. Stud.Appl.Math., 2022, 148 (2), pp.715. ⟨10.1111/sapm.12456⟩. ⟨hal-03287289⟩
73 Consultations
11 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More