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Initial-boundary value problems for the korteweg-de vries equation

Journal Article


Abstract


  • Exact and approximate solutions of the initial-boundary value problem for the Korteweg-de Vries equation on the semi-infinite line are found. These solutions are found for both constant and time-dependent boundary values. The form of the solution is found to depend markedly on the specific boundary and initial value. In particular, multiple solutions and nonsteady solutions are possible. The analytical solutions are compared with numerical solutions of the Korteweg-de Vries equation and are found to be in good agreement. © 1991 Oxford University Press.

Publication Date


  • 1991

Citation


  • Marchant, T. R., & Smyth, N. F. (1991). Initial-boundary value problems for the korteweg-de vries equation. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 47(3), 247-264. doi:10.1093/imamat/47.3.247

Scopus Eid


  • 2-s2.0-0026388453

Start Page


  • 247

End Page


  • 264

Volume


  • 47

Issue


  • 3

Abstract


  • Exact and approximate solutions of the initial-boundary value problem for the Korteweg-de Vries equation on the semi-infinite line are found. These solutions are found for both constant and time-dependent boundary values. The form of the solution is found to depend markedly on the specific boundary and initial value. In particular, multiple solutions and nonsteady solutions are possible. The analytical solutions are compared with numerical solutions of the Korteweg-de Vries equation and are found to be in good agreement. © 1991 Oxford University Press.

Publication Date


  • 1991

Citation


  • Marchant, T. R., & Smyth, N. F. (1991). Initial-boundary value problems for the korteweg-de vries equation. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 47(3), 247-264. doi:10.1093/imamat/47.3.247

Scopus Eid


  • 2-s2.0-0026388453

Start Page


  • 247

End Page


  • 264

Volume


  • 47

Issue


  • 3