Mach-Type Soliton in the Novikov–Veselov Equation

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.