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Compacton and periodic wave solutions of the non-linear dispersive Zakharov-Kuznetsov equation

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In this paper, the nonlinear dispersive Zakharov-Kuznetsov equation is solved by using the sine-cosine method. As a result, compactons, periodic, and singular periodic wave solutions are found.

Collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices

64%

Mihalache D., Mazilu D., Lederer F.

Open Physics

2010

vol. 8

issue 1

77-86

Systematic results of collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices are reported. The generic outcomes are identified for (i) the collision of two identical solitons located in the corner, at the edge, and in the center of the photonic lattice, and for (ii) the collision of two non-identical corner and edge solitons located at different distances from the boundaries of the photonic lattice. Depending on the values of the kick (collision momentum) and of the nonlinear (cubic) gain, the collision scenarios include soliton merging, creation of an extra soliton, soliton bouncing, soliton spreading, and quasi-elastic (symmetric) interactions.

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2 Open Physics

1 2010

1 2007

1 Lederer F.

1 Mazilu D.

1 Mihalache D.

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Compacton and periodic wave solutions of the non-linear dispersive Zakharov-Kuznetsov equation

Collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices