A hierarchy of nonlocal nonlinear evolution equations and partial derivative-dressing method

Starting from the matrix partial derivative problem, the dressing method is employed to investigate the nonlocal nonlinear evolution equations. A hierarchy of nonlocal nonlinear evolution equations associated with 2 x 2 matrix problem, which contains the nonlocal extended modified Korteweg-de Vries (emKdV) equation, is derived via using recursive operator for the first time. Finally, via selecting a proper spectral transformation matrix, the N-soliton solutions of the nonlocal emKdV equation are constructed based on the matrix partial derivative problem. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This article uses the dressing method to investigate nonlocal nonlinear evolution equations starting from the matrix partial derivative problem. A hierarchy of equations associated with 2 x 2 matrix problem is derived, including the nonlocal extended modified Korteweg-de Vries (emKdV) equation. N-soliton solutions of the nonlocal emKdV equation are constructed based on the matrix partial derivative problem by selecting a suitable spectral transformation matrix.