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Special exact soliton solutions for the K(2, 2) equation with non-zero constant pedestal |
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| Authors: | Lina Zhang Aiyong Chen Jiade Tang |
| Affiliation: | a Center of Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, Yunnan 650093, PR China b School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, PR China c Department of Mathematics, Chuxiong University, Chuxiong, Yunnan 675000, PR China |
| Abstract: | Special exact solutions of the K(2, 2) equation, ut + (u2)x + (u2)xxx = 0, are investigated by employing the qualitative theory of differential equations. Our procedure shows that the K(2, 2) equation either has loop soliton, cusped soliton and smooth soliton solutions when sitting on the non-zero constant pedestal limx→±∞u = A ≠ 0, or possesses compacton solutions only when limx→±∞u = 0. Mathematical analysis and numerical simulations are provided for these soliton solutions of the K(2, 2) equation. |
| Keywords: | K(2, 2) equation Single peak soliton Loop soliton Cuspon Compacton Smooth soliton |
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