On a Riemann-Hilbert problem for the negative-order KdV equation

In this paper, we study the initial value problem for the negative order integrable KdV (NKdV) equation by Riemann-Hilbert problem method. The solutions of the NKdV equation are constructed in terms of the solution of a 2 x 2-matric Riemann-Hilbert problem via the asymptotic behavior of the spectral variable at one singularity point, lambda = & INFIN;. And the one-soliton and two-soliton solutions are discussed in detail. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper studies the initial value problem for the negative order integrable KdV equation using the Riemann-Hilbert problem method. The solutions of the NKdV equation are constructed based on the asymptotic behavior of the spectral variable at the singularity point λ = & INFIN;. The one-soliton and two-soliton solutions are discussed in detail.