Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.physleta.2006.11.002
DC FieldValue
dc.titleExact solutions of a nonpolynomially nonlinear Schrödinger equation
dc.contributor.authorParwani, R.
dc.contributor.authorTan, H.S.
dc.date.accessioned2014-10-16T09:24:38Z
dc.date.available2014-10-16T09:24:38Z
dc.date.issued2007-04-26
dc.identifier.citationParwani, R., Tan, H.S. (2007-04-26). Exact solutions of a nonpolynomially nonlinear Schrödinger equation. Physics Letters, Section A: General, Atomic and Solid State Physics 363 (3) : 197-201. ScholarBank@NUS Repository. https://doi.org/10.1016/j.physleta.2006.11.002
dc.identifier.issn03759601
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/96540
dc.description.abstractA nonlinear generalisation of Schrödinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1 + 1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrödinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics. © 2006 Elsevier B.V. All rights reserved.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.physleta.2006.11.002
dc.sourceScopus
dc.typeArticle
dc.contributor.departmentPHYSICS
dc.description.doi10.1016/j.physleta.2006.11.002
dc.description.sourcetitlePhysics Letters, Section A: General, Atomic and Solid State Physics
dc.description.volume363
dc.description.issue3
dc.description.page197-201
dc.description.codenPYLAA
dc.identifier.isiut000245659200005
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