Breathers and rogue waves on the periodic wave background of the nonlocal higher-order Chen-Lee-Liu equation

Through Darboux transformation method, the breathers and the rogue waves on the periodic wave background of the nonlocal higher-order Chen-Lee-Liu (HOCLL) equation are construct. First, we use the odd-fold DT, the even-fold DT and the plane wave seed solution to obtain some new solutions for the nonlocal HOCLL equation. These solutions include single- and double-periodic wave, breather on the single- or the double-periodic wave background. Second, we construct the odd-fold semi-degenerate DT and the even-fold semi-degenerate DT to find the higher-order rogue waves on the single-periodic and the double-periodic wave background, respectively. Finally, by choosing appropriate parametric values, the dynamics of above mentioned solutions are analysed graphically.