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A reliable treatment of the physical structure for the nonlinear equation \(K(m,n)\). (English) Zbl 1072.35580
Summary: The nonlinear equation \(K(m, n)\) is studied for all possible values of \(m\) and \(n\). We show that this equation may exhibit compactons, solitons or periodic solutions. The analysis reveals the change of the physical structure of the solutions as a result of the change of \(m\) and \(n\).

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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