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Article: Completely resonant collision of lumps and line solitons in the Kadomtsev–Petviashvili I equation
| Title | Completely resonant collision of lumps and line solitons in the Kadomtsev–Petviashvili I equation |
|---|---|
| Authors | |
| Keywords | Kadomtsev–Petviashvili hierarchy reduction method Kadomtsev–Petviashvili I equation resonant collision semirational solution |
| Issue Date | 1-Oct-2021 |
| Publisher | Wiley |
| Citation | Studies in Applied Mathematics, 2021, v. 147, n. 3, p. 1007-1035 How to Cite? |
| Abstract | Resonant collisions among localized lumps and line solitons of the Kadomtsev–Petviashvili I (KP-I) equation are studied. The KP-I equation describes the evolution of weakly nonlinear, weakly dispersive waves with slow transverse variations. Lumps can only exist for the KP equation when the signs of the transverse derivative and the weak dispersion in the propagation direction are different, that is, in the KP-I regime. Collisions among lumps and solitons for “integrable” equations are normally elastic, that is, wave shapes are preserved except possibly for phase shifts. For resonant collisions, mathematically the phase shift will become indefinitely large. Physically a lump may be detached (or emitted) from a line soliton, survives for a brief transient period in time, and then merges with the next adjacent soliton. This special lump is thus localized in time as well as the two spatial dimensions, and can be termed a “rogue lump.” By employing a reduction method for the KP hierarchy in conjunction with the Hirota bilinear technique, a general |
| Persistent Identifier | http://hdl.handle.net/10722/344386 |
| ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 1.009 |
-lump/
-line-soliton solution is obtained for the KP-I equation for an arbitrary positive integer 
. For 
, collisions among modes become increasingly complicated, with multiple lumps detaching from one single or different line solitons and then disappearing into the remaining solitons. In terms of applications, such “rogue lumps” represent a mode truly localized both in space and time, and will be valuable in modeling physical problems.
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Rao, Jiguang | - |
| dc.contributor.author | Chow, Kwok Wing | - |
| dc.contributor.author | Mihalache, Dumitru | - |
| dc.contributor.author | He, Jingsong | - |
| dc.date.accessioned | 2024-07-24T13:51:10Z | - |
| dc.date.available | 2024-07-24T13:51:10Z | - |
| dc.date.issued | 2021-10-01 | - |
| dc.identifier.citation | Studies in Applied Mathematics, 2021, v. 147, n. 3, p. 1007-1035 | - |
| dc.identifier.issn | 0022-2526 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/344386 | - |
| dc.description.abstract | <p>Resonant collisions among localized lumps and line solitons of the Kadomtsev–Petviashvili I (KP-I) equation are studied. The KP-I equation describes the evolution of weakly nonlinear, weakly dispersive waves with slow transverse variations. Lumps can only exist for the KP equation when the signs of the transverse derivative and the weak dispersion in the propagation direction are different, that is, in the KP-I regime. Collisions among lumps and solitons for “integrable” equations are normally elastic, that is, wave shapes are preserved except possibly for phase shifts. For resonant collisions, mathematically the phase shift will become indefinitely large. Physically a lump may be detached (or emitted) from a line soliton, survives for a brief transient period in time, and then merges with the next adjacent soliton. This special lump is thus localized in time as well as the two spatial dimensions, and can be termed a “rogue lump.” By employing a reduction method for the KP hierarchy in conjunction with the Hirota bilinear technique, a general <img alt="urn:x-wiley:00222526:media:sapm12417:sapm12417-math-0001" src="https://onlinelibrary.wiley.com/cms/asset/beccd2aa-7db8-4150-8242-5f6e27053785/sapm12417-math-0001.png">-lump/<img alt="urn:x-wiley:00222526:media:sapm12417:sapm12417-math-0002" src="https://onlinelibrary.wiley.com/cms/asset/c052860a-f0e2-4095-b1c8-2f325802ddc1/sapm12417-math-0002.png">-line-soliton solution is obtained for the KP-I equation for an arbitrary positive integer <img alt="urn:x-wiley:00222526:media:sapm12417:sapm12417-math-0003" src="https://onlinelibrary.wiley.com/cms/asset/741b380f-4962-4480-89ff-4586edc43e8f/sapm12417-math-0003.png">. For <img alt="urn:x-wiley:00222526:media:sapm12417:sapm12417-math-0004" src="https://onlinelibrary.wiley.com/cms/asset/7db8d8c5-95c6-43be-88e9-860259bfcbfb/sapm12417-math-0004.png">, collisions among modes become increasingly complicated, with multiple lumps detaching from one single or different line solitons and then disappearing into the remaining solitons. In terms of applications, such “rogue lumps” represent a mode truly localized both in space and time, and will be valuable in modeling physical problems.<br></p> | - |
| dc.language | eng | - |
| dc.publisher | Wiley | - |
| dc.relation.ispartof | Studies in Applied Mathematics | - |
| dc.subject | Kadomtsev–Petviashvili hierarchy reduction method | - |
| dc.subject | Kadomtsev–Petviashvili I equation | - |
| dc.subject | resonant collision | - |
| dc.subject | semirational solution | - |
| dc.title | Completely resonant collision of lumps and line solitons in the Kadomtsev–Petviashvili I equation | - |
| dc.type | Article | - |
| dc.identifier.doi | 10.1111/sapm.12417 | - |
| dc.identifier.scopus | eid_2-s2.0-85108361120 | - |
| dc.identifier.volume | 147 | - |
| dc.identifier.issue | 3 | - |
| dc.identifier.spage | 1007 | - |
| dc.identifier.epage | 1035 | - |
| dc.identifier.eissn | 1467-9590 | - |
| dc.identifier.issnl | 0022-2526 | - |