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Korteweg-de Vries equation and generalizations. I: A remarkable explicit nonlinear transformation. (English) Zbl 0283.35018
Summary: An explicit nonlinear transformation relating solutions of the Korteweg–de Vries equation and a similar nonlinear equation is presented. This transformation is generalized to solutions of a one-parameter family of similar nonlinear equations. A transformation is given which relates solutions of a “forced” Korteweg–de Vries equation to those of the Korteweg–de Vries equation.

35Q53 KdV equations (Korteweg-de Vries equations)
35A22 Transform methods (e.g., integral transforms) applied to PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Full Text: DOI
[1] DOI: 10.1080/14786449508620739
[2] DOI: 10.1103/PhysRevLett.17.996
[3] DOI: 10.1063/1.1664701 · Zbl 0283.35019
[4] DOI: 10.1002/cpa.3160030302 · Zbl 0039.10403
[5] Cole J. D., Quart. Appl. Math. 9 pp 225– (1951) · Zbl 0043.09902
[6] DOI: 10.1143/JPSJ.24.941
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