Abstract
A variational formulation is extremely difficult to be established for a strongly nonlinear problem, and it is almost impossible for a singular differential equation without linear terms. This paper gives a universal approach to the establishment of a variational formulation of a singular travelling wave by the semi-inverse method. The basic properties of rogue waves are elucidated in an energy frame, and a Hamilton-like conversation law is proposed, which can be used for numerical treatment at the singular point.
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