{"paper":{"title":"Perturbative nonlinear J-matrix method of scattering in two dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A perturbative nonlinear J-matrix method yields the scattering matrix for the two-dimensional nonlinear Schrödinger equation with circular symmetry and detects energy-dependent bifurcations.","cross_cats":["nlin.SI"],"primary_cat":"quant-ph","authors_text":"A. D. Alhaidari, T. J. Taiwo, U. Al Khawaja","submitted_at":"2025-11-18T14:15:26Z","abstract_excerpt":"We introduce a perturbative formulation for a nonlinear extension of the J-matrix method of scattering in two dimensions. That is, we obtain the scattering matrix for the time-independent nonlinear Schr\\\"odinger equation in two dimensions with circular symmetry. The formulation relies on the linearization of products of orthogonal polynomials and on the utilization of the tools of the J-matrix method. Gauss quadrature integral approximation is instrumental in the numerical implementation of the approach. We present the theory for a general \\psi ^{2n + 1} nonlinearity, where n is a natural numb"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We obtain the scattering matrix for the time-independent nonlinear Schrödinger equation in two dimensions with circular symmetry... At certain value(s) of the energy, we observe the occurrence of bifurcation with two stable solutions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The linearization of products of orthogonal polynomials remains accurate enough under the perturbative treatment to capture the essential nonlinear effects without introducing uncontrolled errors in the scattering matrix or the bifurcation points.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A perturbative extension of the J-matrix method yields scattering matrices for the 2D nonlinear Schrödinger equation with ψ³ and ψ⁵ nonlinearities, exhibiting bifurcations at specific energies.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A perturbative nonlinear J-matrix method yields the scattering matrix for the two-dimensional nonlinear Schrödinger equation with circular symmetry and detects energy-dependent bifurcations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d10921aac64bcbe5ec942af8e590f61857b924c96f98f0cd2d5c6e9e5174083b"},"source":{"id":"2511.14519","kind":"arxiv","version":1},"verdict":{"id":"94a89859-90f2-4838-b7e1-63eec0c67a9d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T20:51:17.204558Z","strongest_claim":"We obtain the scattering matrix for the time-independent nonlinear Schrödinger equation in two dimensions with circular symmetry... At certain value(s) of the energy, we observe the occurrence of bifurcation with two stable solutions.","one_line_summary":"A perturbative extension of the J-matrix method yields scattering matrices for the 2D nonlinear Schrödinger equation with ψ³ and ψ⁵ nonlinearities, exhibiting bifurcations at specific energies.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The linearization of products of orthogonal polynomials remains accurate enough under the perturbative treatment to capture the essential nonlinear effects without introducing uncontrolled errors in the scattering matrix or the bifurcation points.","pith_extraction_headline":"A perturbative nonlinear J-matrix method yields the scattering matrix for the two-dimensional nonlinear Schrödinger equation with circular symmetry and detects energy-dependent bifurcations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.14519/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":28,"sample":[{"doi":"","year":2019,"title":"G. P. Agrawal, Nonlinear Fiber Optics, 6th ed. (San Diego: Academic Press, 2019)","work_id":"e563543b-ba9d-4685-bcdf-a704e426d959","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"S. B. Pope, Turbulent Flows (Cambridge: Cambridge University Press, 2000)","work_id":"1107dc3a-fb7c-442c-b3b2-d1e89c18020b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"M. Kono and M. M. Skoric, Nonlinear Physics of Plasmas (Berlin: Springer, 2010)","work_id":"8a46ea5b-6418-4c66-b4fe-0ea5775d80ae","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2nd ed. (Oxford: Oxford University Press, 2000)","work_id":"26f2250e-395a-4e4b-bd77-388fd6c942ff","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"P. G. Kevrekidis, D . J. Frantzeskakis, and R . Carretero-González (Eds.) Emergent Nonlinear Phenomena in Bose -Einstein Condensates: Theory and Experiment (Berlin: Springer, 2008)","work_id":"df565d1b-5a4d-4a82-9a1b-22951a7492e4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":28,"snapshot_sha256":"62c5a16096f44f3e8d5c8f6cad9e8bcd9ab8e8a50fed43b29f1ec9003dc57893","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9c8849e300e5a1eaeb7949abc891191e8b909a6a3a551c78c45a29ddfeaaa21f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}