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Linear Limit Continuation: Theory and an Application to Two-Dimensional Bose-Einstein Condensates

https://doi.org/10.2139/ssrn.4675632
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32/32 checkable references clean · checked 2026-07-25

Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.

12 without a DOI — not checked. A reference deposited without a DOI is never matched by title or guessed at; it stays outside the checked set, and this line discloses that.

The 32 checked references that resolve
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The Defocusing Nonlinear Schrödinger Equation
resolves10.1201/b18346
Superfluid States of Matter
resolves10.1103/RevModPhys.81.647
Rotating trapped Bose-Einstein condensates
resolves10.1103/RevModPhys.78.179
Dynamics of Bose-Einstein condensates in optical lattices
resolves10.1038/nphys962
Oscillations and interactions of dark and dark–bright solitons in Bose–Einstein condensates
resolves10.1103/PhysRevLett.125.170401
Collisions of Three-Component Vector Solitons in Bose-Einstein Condensates
resolves10.1142/S0217984904007967
VORTICES IN BOSE–EINSTEIN CONDENSATES: SOME RECENT DEVELOPMENTS
resolves10.1103/PhysRevLett.118.244101
Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments
resolves10.1016/j.cnsns.2017.05.024
Computing stationary solutions of the two-dimensional Gross–Pitaevskii equation with deflated continuation
resolves10.1016/j.cnsns.2020.105255
Bifurcation analysis of stationary solutions of two-dimensional coupled Gross–Pitaevskii equations using deflated continuation
resolves10.1142/S0217979205032279
DYNAMICS OF BRIGHT MATTER WAVE SOLITONS IN A BOSE–EINSTEIN CONDENSATE
resolves10.1088/1751-8113/43/21/213001
Dark solitons in atomic Bose–Einstein condensates: from theory to experiments
resolves10.1103/PhysRevLett.92.230401
Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction
resolves10.1103/PhysRevA.95.043638
Single and multiple vortex rings in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics
resolves10.1103/PhysRevA.105.013319
Instabilities of a vortex-ring-bright soliton in trapped binary three-dimensional Bose-Einstein condensates
resolves10.1088/0951-7715/28/9/3243
Darboux transformation and multi-dark soliton for<i>N</i>-component nonlinear Schrödinger equations
resolves10.1103/PhysRevE.74.056608
Symmetry breaking in symmetric and asymmetric double-well potentials
resolves10.1103/PhysRevA.82.013646
Bifurcations, stability, and dynamics of multiple matter-wave vortex states
resolves10.1103/PhysRevA.77.023625
Radially symmetric nonlinear states of harmonically trapped Bose-Einstein condensates
resolves10.1088/1361-6455/abe67d
Dark–dark soliton breathing patterns in multi-component Bose–Einstein condensates
resolves10.1103/PhysRevE.104.014217
Systematic vector solitary waves from their linear limits in one-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> -component Bose-Einstein condensates
resolves10.1088/1361-6455/acdb16
Systematic solitary waves from their linear limits in two-component Bose–Einstein condensates with unequal dispersion coefficients
resolves10.1103/PhysRevA.100.053621
Ring dark solitons in three-dimensional Bose-Einstein condensates
resolves10.1088/1361-6455/ac69c0
Controlled engineering of a vortex-bright soliton dynamics using a constant driving force
resolves10.1103/PhysRevA.92.033611
Stabilization of ring dark solitons in Bose-Einstein condensates
resolves10.1103/PhysRevA.81.023627
Distribution of eigenfrequencies for oscillations of the ground state in the Thomas-Fermi limit
resolves10.1103/PhysRevA.95.043618
Generation of dark solitons and their instability dynamics in two-dimensional condensates
resolves10.1103/PhysRevA.96.043612
Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates
resolves10.1016/j.physd.2011.06.002
Emergence and stability of vortex clusters in Bose–Einstein condensates: A bifurcation approach near the linear limit
resolves10.1103/PhysRevLett.104.160401
Observation of Vortex Dipoles in an Oblate Bose-Einstein Condensate
resolves10.1103/PhysRevLett.110.200406
Bose-Einstein Condensation of Atoms in a Uniform Potential
resolves10.1103/PhysRevE.107.044215
Polygons of quantized vortices in Bose-Einstein condensates with a circular trap
The 12 references without a DOI — listed, not checked
no DOI — not checkedref1
no DOI — not checkedref2
no DOI — not checkedref5
no DOI — not checkedref7
no DOI — not checkedDeflation-based identification of nonlinear excitations of the three-dimensional Gross-Pitaevskii equation
no DOI — not checkedStability and dispersion relations of three-dimensional solitary waves in trapped Bose-Einstein condensates
no DOI — not checkedThree-dimensional parallel vortex rings in Bose-Einstein condensates
no DOI — not checkedChladni Solitons and the Onset of the Snaking Instability for Dark Solitons in Confined Superfluids
no DOI — not checkedDark spherical shell solitons in threedimensional Bose-Einstein condensates: Existence, stability, and dynamics
no DOI — not checkedPairwise interactions of ring dark solitons with vortices and other rings: Stationary states, stability features, and nonlinear dynamics
no DOI — not checkedCoherent disintegration and stability of vortices in trapped Bose condensates
no DOI — not checkedControlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier
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