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The （G′/G）-expansion method is extended to construct non-traveling wave solutions and explore the fractal structure for high dimensional nonlinear physical equation. As an example, a series of non-traveling solutions is obtained for the （2+1）-dimensional dispersive long wave system with variable coefficient. Furthermore, by setting properly the arbitrary functions in the solutions, a class of novel fractal structures, namely, the cross-like fractal structures are firstly observed.
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Keywords:
- （G′/G）-expansion method/
- （2+1）-dimensional dispersive long wave system with variable coefficient/
- non-traveling solution/
- cross-like fractal structure
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