Initial-Boundary Value Problems for the Korteweg-de Vries Equation

Exact and approximate solutions of the initial—boundaryvalue problem for the Korteweg—de Vries equation on thesemi-infinite line are found. These solutions are found forboth constant and time-dependent boundary values. The form ofthe solution is found to depend markedly on the specific boundaryand initial value. In particular, multiple solutions and nonsteadysolutions are possible. The analytical solutions are comparedwith numerical solutions of the Korteweg—de Vries equationand are found to be in good agreement.