Paper Citation Record · LEDGER

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach

As of 12 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2502.07682.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2502.07682 v3

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T12:03:20.961554Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

27 of 27 outbound references displayed

verified exact0
verified fuzzy14
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5fc34cba-bf98-4c00-92ca-3e91e08e1b44 · outbound

This paper cites Zakharov, E.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Zakharov, E

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.450502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 223921d4-b814-445d-982d-d7d8ce4e383b · outbound

This paper cites Wazwaz, Partial differential equations and solitary waves theory, Springer Science & Business Media, 2010.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Wazwaz, Partial differential equations and solitary waves theory, Springer Science & Business Media, 2010

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.433479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6f59907d-1ad5-45bc-bb9b-40826d01e5f9 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.415612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d079f987-75c6-4f79-a140-7967a659bb5b · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.398571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 95c6b27e-b333-4b18-b2c0-1ad5b78e3a13 · outbound

This paper cites Niwas, S.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Niwas, S

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.382061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ae89ffea-aa74-43fb-8fc8-711c0a9c14c6 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.365466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 62689aab-24d0-483c-814b-c7ecd62b6777 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.347744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 45c15d32-04ad-4685-b1c2-1f05fd24a2fc · outbound

This paper cites Fritzsche, Sophus Lie, Journal of Lie Theory 9 (1999) 1–38.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Fritzsche, Sophus Lie, Journal of Lie Theory 9 (1999) 1–38

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.331175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cc7a2d39-fc9c-4e02-a592-489a2331fe5d · outbound

This paper cites Helgason, Sophus Lie, the mathematician, in: The Sophus Lie Memorial Conference, Scandinavian Univ.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Helgason, Sophus Lie, the mathematician, in: The Sophus Lie Memorial Conference, Scandinavian Univ

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.314384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation aa9ecdbf-e7dd-4953-8e3a-5a67e4ea12dd · outbound

This paper cites Schwarz, Symmetries of differential equations: from Sophus Lie to computer algebra, SIAM Review 30 (3) (1988) 450–481.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Schwarz, Symmetries of differential equations: from Sophus Lie to computer algebra, SIAM Review 30 (3) (1988) 450–481

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.297450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a49722ba-67b4-4ddd-a809-6586c4e370d8 · outbound

This paper cites Lou, H.-C.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Lou, H.-C

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.282597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8f3a0334-4e35-4401-9171-6e06683d1878 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.267065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 466d1f32-e245-4f40-a02d-0b35f9b42760 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.251537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2b6d9e44-fd9c-4c2c-88cc-1c9d9b8ab21d · outbound

This paper cites Kosmann-Schwarzbach, et al., Groups and Symmetries, Universitext, Springer, New York (2010).

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Kosmann-Schwarzbach, et al., Groups and Symmetries, Universitext, Springer, New York (2010)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.236129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 90c60fe0-0d12-4aa1-90e2-6815a86f9475 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.219352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fae22c88-dd99-4177-b7ec-c9be4c4363da · outbound

This paper cites Bluman, Simplifying the form of Lie groups admitted by a given differential equation, Journal of Mathematical Analysis and Applications 145 (1) (1990) 52–62.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Bluman, Simplifying the form of Lie groups admitted by a given differential equation, Journal of Mathematical Analysis and Applications 145 (1) (1990) 52–62

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.202959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4d4cb9b0-bd60-41f4-8155-eeb606ab4053 · outbound

This paper cites Tracin` a, On the nonlinear self-adjointness of the Zakharov–Kuznetsov equation, Communications in Nonlinear Science and Numerical Simulation 19 (2) (2014) 377–382.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Tracin` a, On the nonlinear self-adjointness of the Zakharov–Kuznetsov equation, Communications in Nonlinear Science and Numerical Simulation 19 (2) (2014) 377–382

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.184979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a9aa4bf3-b22e-4097-a62a-ae3ebde68674 · outbound

This paper cites Kosmann-Schwarzbach, B.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Kosmann-Schwarzbach, B

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.165590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 42a3874e-c950-42e5-8e09-9c319ef148e1 · outbound

This paper cites E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-08T12:03:20.919908Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2653c287-fd13-4d86-a53e-d959a966ec4a · outbound

This paper cites Naz, Conservation laws for some systems of nonlinear partial differential equations via multiplier approach, Journal of Applied Mathematics 2012 (1) (2012) 871253.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Naz, Conservation laws for some systems of nonlinear partial differential equations via multiplier approach, Journal of Applied Mathematics 2012 (1) (2012) 871253

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.149446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 23c34e1a-2d14-461a-9ee3-73adffef7310 · outbound

This paper cites Yasar, Y.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Yasar, Y

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.131847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1d38b603-72ca-43e8-91ef-f2dd4589a1ba · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.114322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f09b1e61-fd8b-460c-9dd1-811f841c20c6 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.095432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d571504d-bdb3-4821-ac08-c504e6588752 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.076859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5e8ec38b-acfd-4fb4-9c8d-477761310170 · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.058121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f999af59-b801-467a-86f4-8275b7d7752e · outbound

This paper cites an unresolved cited work.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-08T12:03:21.041042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1fe4a635-be25-4e75-accd-dd3187f76b9e · outbound

This paper cites Qawaqneh, J.

Soliton Dynamics and Modulation Instability in the (3+1)-dimensional ZK equation: A Lie Symmetry Approach Qawaqneh, J

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T12:03:21.021914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.