On the three-dimensional three-wave equation with self-consistent sources

Juan Hu; Xing Biao Hu; Hon Wah TAM

doi:10.1016/j.physleta.2012.06.007

On the three-dimensional three-wave equation with self-consistent sources

Juan Hu^*, Xing Biao Hu, Hon Wah TAM

^*Corresponding author for this work

Department of Computer Science

Research output: Contribution to journal › Journal article › peer-review

4 Citations (Scopus)

Abstract

In this Letter, a three-dimensional three-wave equation with self-consistent sources (3D3W ESCS) is constructed via the source generation procedure. The corresponding Grammian determinant solutions are then derived. As a simple case, the (1,1,1)-lump solution is subsequently examined. A new feature of this 3D3W ESCS is that we allow (a₁X₁+a ₂X₂+a₃X₃)-dependence of the arbitrary constants in the determinant solution for the three-dimensional three-wave equation while applying the source generation procedure. Finally, we show how this new system is reduced to other systems with self-consistent sources.

Original language	English
Pages (from-to)	2402-2407
Number of pages	6
Journal	Physics Letters A
Volume	376
Issue number	35
DOIs	https://doi.org/10.1016/j.physleta.2012.06.007
Publication status	Published - 16 Jul 2012

User-Defined Keywords

Determinant solution
Self-consistent sources
Source generation procedure
Three-dimensional three-wave equation

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10.1016/j.physleta.2012.06.007

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title = "On the three-dimensional three-wave equation with self-consistent sources",

abstract = "In this Letter, a three-dimensional three-wave equation with self-consistent sources (3D3W ESCS) is constructed via the source generation procedure. The corresponding Grammian determinant solutions are then derived. As a simple case, the (1,1,1)-lump solution is subsequently examined. A new feature of this 3D3W ESCS is that we allow (a1X1+a 2X2+a3X3)-dependence of the arbitrary constants in the determinant solution for the three-dimensional three-wave equation while applying the source generation procedure. Finally, we show how this new system is reduced to other systems with self-consistent sources.",

keywords = "Determinant solution, Self-consistent sources, Source generation procedure, Three-dimensional three-wave equation",

author = "Juan Hu and Hu, {Xing Biao} and TAM, {Hon Wah}",

note = "Funding Information: One of the authors (Juan Hu) would like to express her thanks to the anonymous referee for the helpful comments and valuable advices. This work was partially supported by the National Natural Science Foundation of China (Grant No. 11071241 ), the knowledge innovation program of the Institute of Computational Math. , AMSS , and Hong Kong Research Grant Council grant HKBU202209 .",

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doi = "10.1016/j.physleta.2012.06.007",

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T1 - On the three-dimensional three-wave equation with self-consistent sources

AU - Hu, Juan

AU - Hu, Xing Biao

AU - TAM, Hon Wah

N1 - Funding Information: One of the authors (Juan Hu) would like to express her thanks to the anonymous referee for the helpful comments and valuable advices. This work was partially supported by the National Natural Science Foundation of China (Grant No. 11071241 ), the knowledge innovation program of the Institute of Computational Math. , AMSS , and Hong Kong Research Grant Council grant HKBU202209 .

PY - 2012/7/16

Y1 - 2012/7/16

N2 - In this Letter, a three-dimensional three-wave equation with self-consistent sources (3D3W ESCS) is constructed via the source generation procedure. The corresponding Grammian determinant solutions are then derived. As a simple case, the (1,1,1)-lump solution is subsequently examined. A new feature of this 3D3W ESCS is that we allow (a1X1+a 2X2+a3X3)-dependence of the arbitrary constants in the determinant solution for the three-dimensional three-wave equation while applying the source generation procedure. Finally, we show how this new system is reduced to other systems with self-consistent sources.

AB - In this Letter, a three-dimensional three-wave equation with self-consistent sources (3D3W ESCS) is constructed via the source generation procedure. The corresponding Grammian determinant solutions are then derived. As a simple case, the (1,1,1)-lump solution is subsequently examined. A new feature of this 3D3W ESCS is that we allow (a1X1+a 2X2+a3X3)-dependence of the arbitrary constants in the determinant solution for the three-dimensional three-wave equation while applying the source generation procedure. Finally, we show how this new system is reduced to other systems with self-consistent sources.

KW - Determinant solution

KW - Self-consistent sources

KW - Source generation procedure

KW - Three-dimensional three-wave equation

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U2 - 10.1016/j.physleta.2012.06.007

DO - 10.1016/j.physleta.2012.06.007

M3 - Journal article

AN - SCOPUS:84863203925

SN - 0375-9601

VL - 376

SP - 2402

EP - 2407

JO - Physics Letters A

JF - Physics Letters A

IS - 35

ER -

On the three-dimensional three-wave equation with self-consistent sources

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