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.

Item Type:	Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Additional Information:	Author version not held.
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
Subjects:	240000 Physical Sciences > 240500 Classical Physics > 240501 Acoustics and Acoustical Devices; Waves 230000 Mathematical Sciences > 239900 Other Mathematical Sciences > 239999 Mathematical Sciences not elsewhere classified 230000 Mathematical Sciences > 230100 Mathematics > 230107 Differential, Difference and Integral Equations
Socio-Economic Objective (SEO2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
ID Code:	5722
Deposited By:	Assoc Prof Yury Stepanyants
Deposited On:	25 May 2010 23:08
Last Modified:	26 Mar 2012 08:40

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