In this paper, we study the symmetric travelling wave solutions of the b-family of the Novikov equation. We show that the b-family of the Novikov equation can provide symmetric travelling wave solutions, such as peakon, kink and smooth soliton solutions. In particular, the single peakon, two-peakon, stationary kink, anti-kink, two-kink, two-anti-kink, bell-shape soliton and hat-shape soliton solutions are presented in an explicit formula.

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关于Novikov方程b族的解

在本文中，我们研究了 Novikov 方程b族的对称行波解。我们表明，Novikov 方程的b族可以提供对称行波解，例如峰值、扭结和平滑孤子解。特别地，单峰、双峰、平稳扭结、反扭结、双扭结、双反扭结、钟形孤子和帽形孤子解都以显式公式表示。