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Family of nonlinear wave equations which yield loop solutions and solitary wave solutions

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  • This paper gives a family of nonlinear wave equations, which can yield so called loop solution, cusp wave solution and solitary wave solution depending on the values of parameter $A$. For two third order systems, the dynamical behavior of these solutions are considered. The exact explicit parametric representations of solitary wave solutions and periodic wave solutions are given. It concerns with the properties of singular traveling wave systems.
    Mathematics Subject Classification: 34A05, 34C25-28, 34M55, 35Q51, 35Q53, 58F05, 58F14, 58F30.


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