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

arXiv:hep-th/0305252 · Physics Letters A

Bound and anti-bound soliton states for a quantum integrable derivative nonlinear Schrödinger model

B. Basu-Mallick, Tanaya Bhattacharyya, Diptiman Sen

Published Apr 22, 2004• 11 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2004.04.010

Related papers

Novel multi-band quantum soliton states for a derivative nonlinear Schrödinger model

B. Basu-Mallick, Tanaya Bhattacharyya, Diptiman Sen

arXiv:hep-th/0307134•Nuclear Physics B•Oct 17, 2003•8 citations

Exact Solvability and Quantum Integrability of a Derivative Nonlinear Schrödinger Model

B. Basu-Mallick, Tanaya Bhattacharyya

arXiv:hep-th/0308054•Czechoslovak Journal of Physics•Nov 1, 2003•0 citations

Jost solutions and quantum conserved quantities of an integrable derivative nonlinear Schrödinger model

B. Basu-Mallick, Tanaya Bhattacharyya

arXiv:hep-th/0304063•Nuclear Physics B•Jul 31, 2003•14 citations

Solitons in the nonlinear Schrödinger model and the collective ground state of a one-dimensional delta-function gas

Hideaki Hiro-Oka, Hisakazu Minakata

arXiv:hep-th/9405062•Physics Letters A•Dec 1, 1994•1 citation

Algebraic Bethe ansatz for a quantum integrable derivative nonlinear Schrödinger model

B. Basu-Mallick, Tanaya Bhattacharyya

arXiv:hep-th/0202035•Nuclear Physics B•Jul 1, 2002•15 citations

Nonperturbative studies of a quantum higher-order nonlinear Schrödinger model using the Bethe ansatz

Alexander Shnirman, Boris A. Malomed, Eshel Ben‐Jacob

We consider the integrability problem for a quantum version of the perturbed nonlinear Schr\"odinger (NS) equation, including a higher spatial dispersion and nonlinear dispersion of the group velocity (the corresponding classical equations are well known in the nonlinear fiber optics and in other applications). Employing the Bethe ansatz (BA) technique, which is known to yield a complete spectrum including the so-called quantum solitons (multiparticle bound states) of the unperturbed NS system, we find that the particular cases of the model which correspond to integrable classical equations, viz., the derivative NS and Hirota equations, are also fully integrable at the quantum level. In the generic (nonintegrable) case, the model remains integrable in the two-particle sector. In the three-particle sector, the BA produces unphysical states with complex energy. It turns out that the Hamiltonian in this case becomes non-Hermitian. We propose a procedure for finding the physical eigenstates of the system. We build an example of such a state and we show that it describes inelastic scattering.

Physical Review A•Oct 1, 1994•35 citations
We consider the integrability problem for a quantum version of the perturbed nonlinear Schr\"odinger (NS) equation, including a higher spatial dispersion and nonlinear dispersion of the group velocity (the corresponding classical equations are well known in the nonlinear fiber optics and in other applications). Employing the Bethe ansatz (BA) technique, which is known to yield a complete spectrum including the so-called quantum solitons (multiparticle bound states) of the unperturbed NS system, we find that the particular cases of the model which correspond to integrable classical equations, viz., the derivative NS and Hirota equations, are also fully integrable at the quantum level. In the generic (nonintegrable) case, the model remains integrable in the two-particle sector. In the three-particle sector, the BA produces unphysical states with complex energy. It turns out that the Hamiltonian in this case becomes non-Hermitian. We propose a procedure for finding the physical eigenstates of the system. We build an example of such a state and we show that it describes inelastic scattering.