Linear superposition and interaction of Wronskian solutions to an extended (2+1)-dimensional KdV equation

Author:

Cheng Li12,Zhang Yi3,Hu Ying-Wu1

Affiliation:

1. Normal School, Jinhua Polytechnic, Jinhua 321007, China

2. Key Laboratory of Crop Harvesting Equipment Technology, Jinhua Polytechnic, Jinhua 321007, China

3. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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