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Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
Journal of Mathematical Physics · 1968 · Vol. 9(8) · pp. 1202–1204
Robert M. Miura✉(Princeton University)
Abstract
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.
Nonlinear Waves and SolitonsNonlinear Photonic SystemsGeophysics and Sensor TechnologyKorteweg–de Vries equationTransformation (genetics)MathematicsDispersionless equationNonlinear systemKadomtsev–Petviashvili equationBurgers' equationMathematical analysisMathematical physicsApplied mathematics
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References
Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
Journal of Mathematical Physics · 1968 · 988 citations
Reductive Perturbation Method in Nonlinear Wave Propagation. I
Journal of the Physical Society of Japan · 1968 · 551 citations
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