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Linear superposition solutions to nonlinear wave equations |
| Liu Yu (刘煜 ) |
| Henan Electric Power Research Institute, Zhengzhou 450052, China |
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Abstract The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structure characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n,n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed.
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Received: 12 April 2012
Revised: 22 May 2012
Accepted manuscript online:
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PACS:
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02.30.Jr
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(Partial differential equations)
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Corresponding Authors:
Liu Yu
E-mail: ly_hndl@yahoo.com.cn
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Cite this article:
Liu Yu (刘煜 ) Linear superposition solutions to nonlinear wave equations 2012 Chin. Phys. B 21 110205
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