In this paper, solutions of a Novikov equation are discussed based on the bifurcation method of dynamical systems. Through establishing a Hamiltonian function, the existence of a smooth soliton solution and a periodic cuspon solution are established for the corresponding traveling wave system of the Novikov equation. Numerical results are carried out to illustrate the feasibility of the main results. All these theories can be seen to fill the gap of the literatures Li (2014) and Pan and Li (2016).

中文翻译：

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Novikov方程的光滑孤子解和周期cuspon解

本文基于动力学系统的分岔方法，讨论了诺维科夫方程的解。通过建立哈密顿函数，为Novikov方程的相应行波系统建立了一个光滑孤子解和一个周期性cuspon解的存在。数值结果表明了主要结果的可行性。可以看出所有这些理论填补了文献Li（2014）和Pan and Li（2016）的空白。