A parametric method of the inverse scattering problem for a general Korteweg-de~Vries equation in halfspace (Q2782073)

This paper deals with the Korteweg-de Vries equation in the Lax form NEWLINE\[NEWLINE \frac{\partial u(x,t)}{\partial t} = \bigg[-\frac{\partial^2}{\partial x^2} + u(x,t),\;\mu_0M_{2n+1}+ \mu_1M_{2n-1}+\dots + \mu_nM_1\bigg],\tag{1} NEWLINE\]NEWLINE where \([T,G]=TG-GT\) and \(\mu_0,\mu_1,\dots ,\mu_n\) are real parameters. The variable \(x\in[0,\infty)\) and the evolution models (1) are considered for \(t\geq 0\). The author proposes a version of the method of parametric generalization of the inverse scattering problem by introducing parameters into the formulas of the means of the Lax pairs hierarchy [see \textit{I.-P. P. Syroid}, Ukr. Math. J. 42, No. 2, 197-203 (1990; Zbl 0729.47045)].