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
2006-01-01
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.
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