On classical solutions of the KdV equation

Abstract

\begin{abstract} We show that if the initial profile $q\left(x\right)$ for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and ${\int }^{\infty }{x}^{5/2}\left|q\left(x\right)\right|dx<\infty ,$ (no decay at $-\infty$ is required) then the KdV has a unique global classical solution given by a determinant formula. This result is best known to date. \end{abstract}

References in corpus (3)

• On the Numerical Evaluation of Fredholm Determinants
• The Hirota τ-function and well-posedness of the KdV equation with an arbitrary step like initial profile decaying on the right half line
• The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles

Cited by in corpus (5)

• Realization of the inverse scattering transform method for the Korteweg-de Vries equation
• Grassmannian flows and applications to non-commutative non-local and local integrable systems
• The non-commutative Korteweg--de Vries hierarchy and combinatorial Poppe algebra
• Norming constants of embedded bound states and bounded positon solutions of the Korteweg-de Vries equation
• A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditions