Spontaneous transition from flat to cylindrical solitons

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Abstract
Flat, cylindrical, and spherical soliton solutions to various model equations are known. Many of these exact solutions have been seen in numerical simulations. However, there are few simulations that actually show that exact flat solitons can break up into an array of exact cylindrical or spherical solitons and follow this on a step by step basis. This Letter presents the first of these two kinds of transition for the Zakharov-Kuznetsov equation governing ion acoustic solitons in strongly magnetized plasmas.