Dark Korteweg–De Vrise System and Its Higher-Dimensional Deformations
Si-Yu Zhu1, De-Xing Kong1, and Sen-Yue Lou2*
1Zhejiang Qiushi Institute for Mathematical Medicine, Hangzhou 311121, China 2School of Physical Science and Technology, Ningbo University, Ningbo 315211, China
Abstract：The new dimensional deformation approach is proposed to generate higher-dimensional analogues of integrable systems. An arbitrary ($K$+1)-dimensional integrable Korteweg–de Vries (KdV) system, as an example, exhibiting symmetry, is illustrated to arise from a reconstructed deformation procedure, starting with a general symmetry integrable (1+1)-dimensional dark KdV system and its conservation laws. Physically, the dark equation systems may be related to dark matter physics. To describe nonlinear physics, both linear and nonlinear dispersions should be considered. In the original lower-dimensional integrable systems, only liner or nonlinear dispersion is included. The deformation algorithm naturally makes the model also include the linear dispersion and nonlinear dispersion.
2023, Vol. 40 
