Mach-Type Soliton in the Novikov-Veselov Equation
Jen-Hsu Chang
TL;DR
This paper constructs Mach-type solitons for the Novikov-Veselov equation using Pfaffian formulas, analyzes their evolution, and explores their relation to V-shape initial waves, revealing linear growth of Mach stem length and amplitude constraints.
Contribution
It introduces a novel method to construct Mach-type solitons for the Novikov-Veselov equation using Pfaffian minor-summation formulas and analyzes their dynamic properties.
Findings
Mach stem wave amplitude is less than twice the incident wave.
Mach stem length grows linearly with time.
Relations with V-shape initial waves depend on Miles parameter.
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.
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