@article{Luo2026, 
author = {Senyue Luo and Meilan Qiu and Fangfang Deng},
title = {Ill-posedness in        H    s   for a defocusing power-type derivative Schrödinger equation with lower-order linear perturbations},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {8507-8520},
keywords = {DNLS-type equation, solitary waves, ill-posedness},
url = {https://www.sciopen.com/article/10.3934/math.2026350},
doi = {10.3934/math.2026350},
abstract = {This work studied the one-dimensional defocusing power-type derivative Schrödinger equation with lower-order linear perturbations         i        u    t    +      u          x      x        −      i        |    u            |        k        u    x    +  α      u    x    +  β  u  =  0  ,    (  t  ,  x  )  ∈      R    ×      R    ,where    k  ≥  2 and    α  ,  β  ∈      R   are constants. An explicit family of solitary traveling-wave solutions is first constructed within an exactly integrable traveling-wave reduction, and their        H    s   regularity and parameter dependence are characterized. A traveling-wave-based ill-posedness mechanism is then implemented: two solutions associated with nearby parameter sets are produced so that their initial data are arbitrarily close in        H    s  , while their profiles remain separated by a uniform positive lower bound in        H    s   at some positive time. As a result, the solution flow map fails to be uniformly continuous below a certain regularity threshold. These results indicate that the presence of lower-order linear perturbations does not improve the low-regularity stability threshold for this DNLS-type equation.}
}