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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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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