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Wronskians, generalized Wronskians and solutions to the Korteweg-de Vries equation. (English) Zbl 1068.35138
Summary: A bridge going from Wronskian solutions to generalized Wronskian solutions of the Korteweg–de Vries (KdV) equation is built. It is then shown that generalized Wronskian solutions can be viewed as Wronskian solutions. The idea is used to generate positons, negatons and their interaction solutions to the KdV equation. Moreover, general positons and negatons are constructed through the Wronskian formulation. A few new exact solutions to the KdV equation are explicitly presented as examples of Wronskian solutions.

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