TY  - JOUR
AU  - Cheng, Li
AU  - Zhang, Yi
AU  - Hu, Ying-Wu
PY  - 2023
TI  - Linear superposition and interaction of Wronskian solutions to an extended (2+1)-dimensional KdV equation
JO  - AIMS Mathematics
SP  - 16906
EP  - 16925
VL  - 8
IS  - 7
AB  - 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.
UR  - https://doi.org/10.3934/math.2023864
DO  - 10.3934/math.2023864