Traveling Wave Solutions for a Class of One-Dimensional Nonlinear Shallow Water Wave Models
نویسندگان
چکیده
In this paper, we shall study traveling wave solutions for a set of onedimensional nonlinear, nonlocal, evolutionary partial differential equations. This class of equations originally arose at quadratic order in the asymptotic expansion for shallow water waves [4,10]. The famous Korteweg–de Vries equation – which is nonlinear, but local – arises uniquely at linear order in this shallow water wave expansion. At quadratic order, a broad class of asymptotically equivalent equations arises
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