An implicit symmetry constraint of the modified Korteweg-de Vries (mKdV) equation
Ying YOU, Jing YU, Qiao-yun JIANG
Department of Mathematics, Zhejiang University, Hangzhou 310027, China; School of Science, Hangzhou Dianzi University, Hangzhou 310018, China; College of Science, Nantong University, Nantong 226007, China
Abstract In this paper, an implicit symmetry constraint is calculated and its associated binary nonlinearization of the Lax pairs and the adjoint Lax pairs is carried out for the modified Korteweg-de Vries (mKdV) equation. After introducing two new independent variables, we find that under the implicit symmetry constraint, the spatial part and the temporal part of the mKdV equation are decomposed into two finite-dimensional systems. Furthermore we prove that the obtained finite-dimensional systems are Hamiltonian systems and completely integrable in the Liouville sense.
