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On the Nonlinear Schrödinger Equation on the Half Line with Homogeneous Robin Boundary Conditions
Author(s) -
Biondini G.,
Bui A.
Publication year - 2012
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2012.00553.x
Subject(s) - eigenvalues and eigenvectors , boundary value problem , mathematical analysis , mathematics , soliton , robin boundary condition , reflection (computer programming) , transformation (genetics) , homogeneous , boundary (topology) , nonlinear system , line (geometry) , boundary values , position (finance) , mathematical physics , mixed boundary condition , physics , geometry , quantum mechanics , biochemistry , chemistry , combinatorics , computer science , programming language , gene , finance , economics
Boundary value problems for the nonlinear Schrödinger equations on the half line with homogeneous Robin boundary conditions are revisited using Bäcklund transformations. In particular: relations are obtained among the norming constants associated with symmetric eigenvalues; a linearizing transformation is derived for the Bäcklund transformation; the reflection‐induced soliton position shift is evaluated and the solution behavior is discussed. The results are illustrated by discussing several exact soliton solutions, which describe the soliton reflection at the boundary with or without the presence of self‐symmetric eigenvalues.