Certain explicit solutions to the Korteweg–de Vries equation in the first quadrant of the xt-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schrodinger equation. In the reflectionless case such solutions reduce to pure N-soliton solutions. An illustrative example is provided.

Explicit Solutions to the Korteweg-De Vries Equation on the Half Line

VAN DER MEE, CORNELIS VICTOR MARIA
2006

Abstract

Certain explicit solutions to the Korteweg–de Vries equation in the first quadrant of the xt-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schrodinger equation. In the reflectionless case such solutions reduce to pure N-soliton solutions. An illustrative example is provided.
Korteweg–de Vries equation; Inverse scattering transform; Marchenko equation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/15086
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