Lump solutions of 2D generalized Gardner equation

Stepanyants, Y. A. and Ten, I. K. and Tomita, H. (2006) Lump solutions of 2D generalized Gardner equation. In: Conference on Nonlinear Science and Complexity, 7-12 Aug 2006, Beijing, China.

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Abstract

Results of numerical study of lump solutions (2D solitons)of a generalised 2D Gardner equation are presented. To construct such solutions, the Petviashvili is further developed for the evolution equations with the non-power linearity. Solution obtained for different relationships between quadratic and cubic nonlinearity as well as between small-and large-scale dispersions () are compared with the known lump solution for the classical Kadomtsev-Petviashvili equation with positive dispersion. The structure of constructed solutions is analysed in terms of two dimensionless parameters characterising the cubic nonlinearity and large-scale dispersion.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author version not held.
Depositing User: Assoc Prof Yury Stepanyants
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 25 May 2010 13:08
Last Modified: 02 Jul 2013 23:24
Uncontrolled Keywords: non-linear waves; soliton; lumps; Petviashvili method; numerical study; Gardner equation
Fields of Research (FOR2008): 01 Mathematical Sciences > 0105 Mathematical Physics > 010599 Mathematical Physics not elsewhere classified
01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/5722

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