A partial derivative-dressing approach to the Kundu-Eckhaus equation

Starting from a local 2 x 2 matrix partial derivative-equation with non-normalization boundary conditions, the spatial and time spectral problems associated with the Kundu-Eckhaus (KE) equation are derived via two linear constraint equations. The gauge equivalence among the KE equation, NLS equation and Heisenberg chain equation are given. A KE hierarchy with source is proposed by using recursive operator. The N-solitions of the KE equation are constructed based the partial derivative-equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The spatial and time spectral problems associated with the Kundu-Eckhaus (KE) equation are derived via linear constraint equations, a KE hierarchy with source is proposed, N-solitons of the KE equation are constructed, and explicit one- and two-soliton solutions are obtained.