The Hirota-Satsuma coupled KdV equation and a coupled Ito system revisited

Hon Wah Tam; Wen Xiu Ma; Xing Biao Hu; Dao Liu Wang

doi:10.1143/JPSJ.69.45

The Hirota-Satsuma coupled KdV equation and a coupled Ito system revisited

Hon Wah Tam^*
, Wen Xiu Ma
, Xing Biao Hu
, Dao Liu Wang

^*Corresponding author for this work

Department of Computer Science

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

122 Citations (Scopus)

Abstract

The well-known Hirota-Satsuma coupled KdV equation and a coupled Ito system are reviewed. A new type of soliton solutions to these two systems under constant boundary condition at infinity is found. The so-called generalized Hirota-Satsuma coupled KdV system is also considered. Starting from its bilinear forms, we obtain a Bäcklund transformation and the corresponding nonlinear superposition formulae. As a result, soliton solutions first obtained by Satsuma and Hirota can be rederived. Moreover, rational solutions are also given.

Original language	English
Pages (from-to)	45-52
Number of pages	8
Journal	Journal of the Physical Society of Japan
Volume	69
Issue number	1
DOIs	https://doi.org/10.1143/JPSJ.69.45
Publication status	Published - Jan 2000

User-Defined Keywords

Bäcklund transformation
Hirota's method
Integrable systems
Solitons

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10.1143/JPSJ.69.45

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title = "The Hirota-Satsuma coupled KdV equation and a coupled Ito system revisited",

abstract = "The well-known Hirota-Satsuma coupled KdV equation and a coupled Ito system are reviewed. A new type of soliton solutions to these two systems under constant boundary condition at infinity is found. The so-called generalized Hirota-Satsuma coupled KdV system is also considered. Starting from its bilinear forms, we obtain a B{\"a}cklund transformation and the corresponding nonlinear superposition formulae. As a result, soliton solutions first obtained by Satsuma and Hirota can be rederived. Moreover, rational solutions are also given.",

keywords = "B{\"a}cklund transformation, Hirota's method, Integrable systems, Solitons",

author = "Tam, \{Hon Wah\} and Ma, \{Wen Xiu\} and Hu, \{Xing Biao\} and Wang, \{Dao Liu\}",

year = "2000",

month = jan,

doi = "10.1143/JPSJ.69.45",

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TY - JOUR

T1 - The Hirota-Satsuma coupled KdV equation and a coupled Ito system revisited

AU - Tam, Hon Wah

AU - Ma, Wen Xiu

AU - Hu, Xing Biao

AU - Wang, Dao Liu

PY - 2000/1

Y1 - 2000/1

N2 - The well-known Hirota-Satsuma coupled KdV equation and a coupled Ito system are reviewed. A new type of soliton solutions to these two systems under constant boundary condition at infinity is found. The so-called generalized Hirota-Satsuma coupled KdV system is also considered. Starting from its bilinear forms, we obtain a Bäcklund transformation and the corresponding nonlinear superposition formulae. As a result, soliton solutions first obtained by Satsuma and Hirota can be rederived. Moreover, rational solutions are also given.

AB - The well-known Hirota-Satsuma coupled KdV equation and a coupled Ito system are reviewed. A new type of soliton solutions to these two systems under constant boundary condition at infinity is found. The so-called generalized Hirota-Satsuma coupled KdV system is also considered. Starting from its bilinear forms, we obtain a Bäcklund transformation and the corresponding nonlinear superposition formulae. As a result, soliton solutions first obtained by Satsuma and Hirota can be rederived. Moreover, rational solutions are also given.

KW - Bäcklund transformation

KW - Hirota's method

KW - Integrable systems

KW - Solitons

UR - https://www.scopus.com/pages/publications/0034384726

U2 - 10.1143/JPSJ.69.45

DO - 10.1143/JPSJ.69.45

M3 - Journal article

AN - SCOPUS:0034384726

SN - 0031-9015

VL - 69

SP - 45

EP - 52

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

IS - 1

ER -

The Hirota-Satsuma coupled KdV equation and a coupled Ito system revisited

Abstract

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