×

zbMATH — the first resource for mathematics

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.

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.