Details

Giuseppe Saccomandi^[a] and Luigi Vergori^[b]

The only solitary wave that matters: the sech\(^2\)-type

Pages: 213-222
Received: 25 September 2023
Accepted: 25 January 2024
Mathematics Subject Classification: 35Q53, 35L05, 74J35.
Keywords: Solitary waves, exact solutions, qualitative analysis à la Weierstrass.
Authors address:
[a],[b]: University of Perugia, via Goffredo Duranti 93, Perugia, 06125, Italy

This research is partially supported by GNFM of INDAM and by fondo di ricerca di base 2022 of the University of Perugia.

Abstract: In this note we show that on introducing an appropriate point transformation, any solitary wave solution of a \(1+1\) partial differential equation (PDE) in a single unknown is equivalent to the sech\(^2\) soliton of the Korteweg-de Vries (KdV) equation.

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