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.
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)|
|Item Status:||Live Archive|
|Additional Information:||Author version not held.|
|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 :||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:||E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences|
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