Higher-dimensional KdV equations and their soliton solutions

Yu Feng Zhang; Honwah Tam; Jing Zhao

doi:10.1088/0253-6102/45/3/007

Higher-dimensional KdV equations and their soliton solutions

Yu Feng Zhang^*, Honwah Tam, Jing Zhao

^*Corresponding author for this work

Department of Computer Science

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

16 Citations (Scopus)

Abstract

A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of bell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.

Original language	English
Pages (from-to)	411-413
Number of pages	3
Journal	Communications in Theoretical Physics
Volume	45
Issue number	3
DOIs	https://doi.org/10.1088/0253-6102/45/3/007
Publication status	Published - 15 Mar 2006

User-Defined Keywords

Bilinear operator
Kdv equation
Soliton equation

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10.1088/0253-6102/45/3/007

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AU - Tam, Honwah

AU - Zhao, Jing

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N2 - A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of bell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.

AB - A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of bell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.

KW - Bilinear operator

KW - Kdv equation

KW - Soliton equation

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JF - Communications in Theoretical Physics

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Higher-dimensional KdV equations and their soliton solutions

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