Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 111, 14 pages      arXiv:1408.0588      https://doi.org/10.3842/SIGMA.2014.111

Mach-Type Soliton in the Novikov-Veselov Equation

Jen-Hsu Chang
Department of Computer Science and Information Engineering, National Defense University, Tauyuan County 33551, Taiwan

Received September 18, 2014, in final form December 10, 2014; Published online December 18, 2014

Abstract
Using the reality condition of the solutions, one constructs the Mach-type soliton of the Novikov-Veselov equation by the minor-summation formula of the Pfaffian. We study the evolution of the Mach-type soliton and find that the amplitude of the Mach stem wave is less than two times of the one of the incident wave. It is shown that the length of the Mach stem wave is linear with time. One discusses the relations with $V$-shape initial value wave for different critical values of Miles parameter.

Key words: Pfaffian; Mach-type soliton; Mach stem wave; $V$-shape wave.

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