Dark Korteweg-De Vrise System and Its Higher-Dimensional Deformations

The new dimensional deformation approach is proposed to generate higher-dimensional analogues of integrable systems.An arbitrary(K+1)-dimensional integrable Korteweg-de Vries(Kd V)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 Kd V 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.