Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The European Physical Journal D

Eigenvalues of the nonlinear Schrödinger equation

S. Geltman

Published Sep 1, 2012• 0 citations
Publisher
DOI
10.1140/epjd/e2012-30194-1

Related papers

On the Non-Linear Schrödinger Equation

A.B. Datzeff

Springer eBooks•Jan 1, 1985•0 citations

Excitation spectrum and quantum inverse problem for an alternative version of the nonlinear Schrödinger equation

Asesh Roy Chowdhury, Shibani Sen

We have formulated the quantum inverse problem for an alternative version of the nonlinear Schr\"odinger equation (NLS), which is a variant of the derivative NLS (DNLS) equation. While the DNLS equation is nonultralocal and cannot be formulated as a problem of the quantum inverse scattering method, our equation is ultralocal, and hence it is possible to construct the quantum R matrix and the commutation rules for the scattering data. Next we have constructed the algebraic Bethe ansatz, from which the eigenvalue equation for the excited states is derived. This eigenvalue equation admits stringlike configurations, and the density of states corresponding to real and complex eigenvalues is explicitly derived in the thermodynamic limit.

Physical Review A•Feb 1, 1991•3 citations

Exact solutions of the inhomogeneous nonlinear Schrödinger equation through supersymmetric potentials

David J. Fernández C., O. Pavón-Torres

By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schrödinger equation (INLSE). This is possible due to the connection between the INLSE and the nonlinear Schrödinger equation (NLSE), which can be established from a treatment based on Lie point symmetries and is related with Schrödinger equation, under certain conditions. As an illustrative example, we construct exact solutions for the INLSE through a Pösch-Teller potential with a single bound state.

quant-pharXiv:2511.18186•Nov 25, 2025

Some nonlinear extensions for the schrödinger equation

Ervin Kaminski Lenzi, Antonio S. M. de Castro, R. S. Mendes

Chinese Journal of Physics•May 3, 2020•3 citations

Variational solution of the Schrödinger equation

Kálmán Varga, Joseph A. Driscoll

Cambridge University Press eBooks•Apr 14, 2011•0 citations

A unified construction of variational methods for the nonlinear Schrödinger equation

Yeongji Kim, Alexander L. Zubarev

Based on an approach introduced by Gerjuoy, Rau, and Spruch, we construct variational principles in a systematic way for the nonlinear Schrödinger equation and obtain new variational principles for the case of Ginzburg-Pitaevskii-Gross equation (GPG) which is believed to describe accurately the Bose-Einstein condensation at zero temperature. As an application of these variational methods, a variational iteration method is proposed for calculating eigenvalue (chemical potential) and wave function for the GPG equation 1.

Il Nuovo Cimento B•Sep 1, 1998•0 citations
We have formulated the quantum inverse problem for an alternative version of the nonlinear Schr\"odinger equation (NLS), which is a variant of the derivative NLS (DNLS) equation. While the DNLS equation is nonultralocal and cannot be formulated as a problem of the quantum inverse scattering method, our equation is ultralocal, and hence it is possible to construct the quantum R matrix and the commutation rules for the scattering data. Next we have constructed the algebraic Bethe ansatz, from which the eigenvalue equation for the excited states is derived. This eigenvalue equation admits stringlike configurations, and the density of states corresponding to real and complex eigenvalues is explicitly derived in the thermodynamic limit.
By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schrödinger equation (INLSE). This is possible due to the connection between the INLSE and the nonlinear Schrödinger equation (NLSE), which can be established from a treatment based on Lie point symmetries and is related with Schrödinger equation, under certain conditions. As an illustrative example, we construct exact solutions for the INLSE through a Pösch-Teller potential with a single bound state.
Based on an approach introduced by Gerjuoy, Rau, and Spruch, we construct variational principles in a systematic way for the nonlinear Schrödinger equation and obtain new variational principles for the case of Ginzburg-Pitaevskii-Gross equation (GPG) which is believed to describe accurately the Bose-Einstein condensation at zero temperature. As an application of these variational methods, a variational iteration method is proposed for calculating eigenvalue (chemical potential) and wave function for the GPG equation 1.