The Concave or Convex Peaked and Smooth Soliton Solutions of Camassa-Holm Equation
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摘要: 研究一类完全可积的新型浅水波方程Camassa-Holm方程的行波孤立子解及双孤立子解.引入凹凸尖峰孤立子及光滑孤立子的概念,研究得到该方程的行波解中具有尖峰性质的凹凸尖峰孤立子解及光滑孤立子解.同时利用Backlund变换给出该类方程的新的双孤立子解.Abstract: The traveling wave soliton solutions and pair soliton solution to a class of new completely integralbe shallow water equation,Camassa-Holm equation are studied.The concept of concave or convex peaked soliton and smooth soliton were introduced.And the research shows that the traveling wave solution of that equation possesses concave and convex peaked soliton and smooth soliton solutions with the peakson.Simultaneously by applying Backlund transformation the new pair soliton solutions to this class of equation are given.
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Key words:
- soliton /
- peakson /
- integrable system /
- traveling wave solution
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[1] Roberto Camassa,Darryl D Holm.An integrable shallow water equation with peaked solitons[J].Phy Rev Letters,1993,71(13):1661-1664. [2] Alber M S,Camassa R.The geometry of peaked soliton and billiard solutions of a class of integrable PDE's[J].Letters Math Phy,1994,32(2):137-151. [3] Clarkson P A,Mansfield E L,Priestley T J.Symmetries of a class of nonlinear third-order partial differential equations[J].Math Comput Modelling,1997,25(8/9):195-212. [4] XIN Zhou-ping,ZHANG Ping.On the weak solutions to a shallow water equation[J].Comm Pure Appli Math,2000,53(9):1411-1433. [5] Michael Fisher,Jeremy Schiff.The camassa Holm equation:Conserved quantities and the initial value problem[J].Phy Lett A,1999,259(3):371-376. [6] Adrian Constantin,Waner A Atrauss.Stability of peakons[J].Comm Pure Appli Math,2000,53(10):603-610. [7] Adrian Constantin,Joachim Escher.Well-posedness,global existence and blown up phenomena for a periodic quasi-linear hyperbolic equation[J].1998,51(5):475-504. [8] TIAN Li-xin.Wavelet approximate inertial manifold in nonlinear solitary wave equation[J].J Math Phy,2000,41(8):5773-5793. [9] TIAN Li-xin,LIU Zeng-rong.P dissipative operator[J].Comm Math Phy,1999,201(3):509-538. [10] TIAN Li-xin,LIU Zeng-rong.The Schrdinger operator[J].Proc Amer Math Soc,1998,126(1):201-211.
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