@article{Cheng2023, 
author = {Li Cheng and Yi Zhang and Ying-Wu Hu},
title = {Linear superposition and interaction of Wronskian solutions to an extended (2+1)-dimensional KdV equation},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {16906-16925},
keywords = {extended (2+1)-dimensional KdV equation, bilinear Bäcklund transformation, Lax pair, linear superposition solution, Wronskian interaction solution},
url = {https://www.sciopen.com/article/10.3934/math.2023864},
doi = {10.3934/math.2023864},
abstract = {The main purpose of this work is to discuss an extended KdV equation, which can provide some physically significant integrable evolution equations to model the propagation of two-dimensional nonlinear solitary waves in various science fields. Based on the bilinear Bäcklund transformation, a Lax system is constructed, which guarantees the integrability of the introduced equation. The linear superposition principle is applied to homogeneous linear differential equation systems, which plays a key role in presenting linear superposition solutions composed of exponential functions. Moreover, some special linear superposition solutions are also derived by extending the involved parameters to the complex field. Finally, a set of sufficient conditions on Wronskian solutions is given associated with the bilinear Bäcklund transformation. The Wronskian identities of the bilinear KP hierarchy provide a direct and concise way for proving the Wronskian determinant solution. The resulting Wronskian structure generates    N-soliton solutions and a few of special Wronskian interaction solutions, which enrich the solution structure of the introduced equation.}
}