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Two-Mode Wave Solutions to the Degasperis--Procesi Equation |
| ZHANG Zheng-Di, BI Qin-Sheng |
| Faculty of Science, Jiangsu University, Zhenjiang 212013 |
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ZHANG Zheng-Di, BI Qin-Sheng 2008 Chin. Phys. Lett. 25 4211-4214 |
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Abstract By introducing a new type of solutions, called the multiple-mode wave solutions which can be expressed in nonlinear superposition of single-mode waves with different speeds, we investigate the two-mode wave solutions in Degasperis--Procesi equation and two cases are derived. The explicit expressions for the two-mode waves as well as the existence conditions are presented. It is shown that the two-mode waves may be the nonlinear combinations of many types of single-mode waves, such as periodic waves, solitons, compactons, etc., and more complicated multiple-mode waves can be obtained if higher order or more single-mode waves are taken into consideration. It is pointed out that the two-mode wave solutions can be employed to display the typical mechanism of the interactions between different single-mode waves.
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05.45.Yv
05.45.-a
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Received: 08 May 2008
Published: 27 November 2008
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