Darboux Transformation and Exact Solutions of the Variable Coefficient Nonlocal Newell–Whitehead Equation

In this article, the integrable nonlocal nonlinear variable coefficient Newell–Whitehead (NW) equation is investigated for the first time. First, the variable coefficient nonlocal NW equation is constructed with the aid of symmetry reduction and Lax pair. On this basis, the Darboux transformation of the variable coefficient nonlocal NW equation is studied. Then, some exact solutions are obtained by applying the Darboux transformation. The results show that the variable coefficient equation has more general solutions than its constant coefficient form. Finally, the solutions of the variable coefficient nonlocal NW equation are given when the coefficient function takes on special values, and the structural features of the solutions are visualized in images.