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An Approach for Solving Short-Wave Models for Camassa-Holm Equation and Degasperis-Procesi Equation
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作者 YANG Pei CHEN Yong LI Zhi-Bin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第9期583-586,共4页
In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transform... In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach. 展开更多
关键词 Camassa-Holm equation Degasperis-Procesi equation one-cusp soliton one-loop soliton Adomian decomposition method
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A Riemann-Hilbert Approach to the Harry-Dym Equation on the Line 被引量:3
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作者 Yu XIAO Engui FAN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第3期373-384,共12页
In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem... In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem in the complex plane. Further, onecusp soliton solution is expressed in terms of the Riemann-Hilbert problem. 展开更多
关键词 Harry-Dym equation Riemann-Hilbert problem Initial-value problem one-cusp soliton solution
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