A vector asymmetrical NNV equation: Soliton solutions, bilinear Bäcklund transformation and Lax pair

A vector asymmetrical Nizhnik–Novikov–Veselov (NNV) equation is proposed based on its bilinear form. Soliton solutions expressed by Pfaffians are obtained. Bilinear Bäcklund transformation and the corresponding Lax pair for the vector ANNV equation are derived.