Time evolution of perturbed solitons of modified Kadomtsev-Petviashvili equations
ABSTRACT We solve the (2+1)-dimensional Schamel-Kadomtsev- Petviashvili equations with negative and positive dispersion numerically with one or two perturbed plane solitons as initial conditions. In the negative dispersion case, the plane soliton is stable and retains its identity. For the equation with positive dispersion, the plane solitons decay into two- dimensional lump solitons. We show that in contrast to one- dimensional solitons, collisions between two lump solitons are far from elastic. We also demonstrate that the solitons emerging from the collision can be very sensitive to the alignment of the solitons prior to collision.
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ABSTRACT: A modified Kadomtsev–Petviashvili (MKP) equation is proposed. The equation is a weakly two-dimensional generalisation of the Schamel equation. It is shown that one form of this equation arises in the context of the propagation of ion-acoustic waves in a plasma with non-isothermal electrons. The stability of certain plane periodic and solitary travelling wave solutions of the MKP equation to two-dimensional long wavelength perturbations is investigated using the method of Rowlands and Infeld. The results obtained are compared with those for the standard KP equation; some qualitative differences are found.Physica Scripta 04/2006; 55(2):135. · 1.03 Impact Factor
Chapter: Numerical Recipes in C2nd 01/1992; Cambridge University Press.
- Physical Review Letters 11/1966; 17(19):996-998. · 7.73 Impact Factor