This article is cited in 2 papers

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

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.

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

MSC: 35C08; 35A22

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

Language: English

DOI: 10.3842/SIGMA.2014.111

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ArXiv: 1408.0588