Complexiton solutions to the asymmetric Nizhnik–Novikov–Veselov equation

We present new complexiton solutions to the (2 + 1)-dimensional asymmetric Nizhnik–Novikov–Veselov (aNNV) equation by application of the Hirota direct method and the linear superposition principle. We first find hyperbolic function solutions to the corresponding bilinear equation and consequently derive the so-called complexitons. In particular, we construct nonsingular complexiton solutions from positive complexiton solutions of the bilinear form of the nonlinear equation. Finally, we give some illustrative examples and a few concluding remarks.