Abstract
A coupled Chen–Lee–Liu (CLL) system is proposed and its linear Lax pair is given. Many kinds of nonlocal-derivative NLS (DNLS) equations arise from the group symmetry reductions of the coupled CLL system. hat{P}hat{T}hat{C}-symmetry invariant one-soliton solution and periodic two-soliton solution of a two-place DNLS (TDNLS) system are obtained. A group symmetry invariant two-soliton solution of a four-place DNLS (FDNLS) system is worked out. New characteristics of the two-soliton interactions for the TDNLS system and FDNLS system are analyzed.
Highlights
It is well known that many physical problems may occur in two or more places which are linked to each other, which can be called multi-place problem
New nonlocal two-place derivative nonlinear Schrödinger (NLS) (DNLS) (TDNLS) and four-place DNLS (FDNLS) systems are derived based on the coupled Chen–Lee–Liu (CLL) system and the P T C -symmetry group
From the coupled system (4), some different kinds of nonlocal integrable DNLS equations can be obtained by using the P T Csymmetry reductions
Summary
It is well known that many physical problems may occur in two or more places which are linked to each other, which can be called multi-place problem. When the operator fis taken as a special case, many kinds of nonlocal integrable systems can be obtained. New nonlocal two-place DNLS (TDNLS) and four-place DNLS (FDNLS) systems are derived based on the coupled Chen–Lee–Liu (CLL) system and the P T C -symmetry group. 3, the expressions of group-invariant soliton solutions for the nonlocal DNLS system are presented and the multi-soliton solutions of the TDNLS system and the FDNLS system are worked out. From the coupled system (4), some different kinds of nonlocal integrable DNLS equations can be obtained by using the P T Csymmetry reductions. When we take fk = 1, gj = {T , P C , P T } or gj = C , fk = {P , T C , P T C }, a two-place nonlocal DNLS systems can be obtained: qt = qxx + 2(p + q)2(r + s)(pr – qs) + 2q(r + s)(px + qx) + 2 (p + q)(qs – pr) x,.
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