Variable Separation Solutions in (1+1)-Dimensional and (3+1)-Dimensional Systems via Entangled Mapping Approach |
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Authors: | DAI Chao-Qing YAN Cai-Jie ZHANG Jie-Fang |
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Affiliation: | Department of Information Physics, School of Sciences, Zhejiang Forestry University, Lin'an 311300, China Department of Physics, Zhejiang Lishui University, Lishui 323000, China Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China |
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Abstract: | In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1 1)-dimensional and (3 1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1 1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3 1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2 1 )-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables. |
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Keywords: | entangled mapping approach (1 1)-dimensional systems (3 1)-dimensional Burgers system |
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