Xiaoyu Jiao

Publications (5)1.41 Total impact

• Source

  Available from: arxiv.org

  Article: Approximate homotopy symmetry method: Homotopy series solutions to the sixth-order Boussinesq equation

  XiaoYu Jiao, Yuan Gao, SenYue Lou
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  ABSTRACT: An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation, which arises from fluid dynamics. We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders, educing the related homotopy series solutions. Zero-order similarity reduction equations are equivalent to the Painlevé IV type equation or Weierstrass elliptic equation. Higher order similarity solutions can be obtained by solving linear variable coefficients ordinary differential equations. The auxiliary parameter has an effect on the convergence of homotopy series solutions. Series solutions and similarity reduction equations from the approximate symmetry method can be retrieved from the approximate homotopy symmetry method.
  Science in China Series G Physics Mechanics and Astronomy 04/2012; 52(8):1169-1178. · 1.41 Impact Factor
• Source

  Available from: ArXiv

  Article: Approximate homotopy symmetry method and homotopy series solutions to the six-order boussinesq equation

  Xiaoyu Jiao, Yuan Gao, S. Y. Lou
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  ABSTRACT: An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the six-order boussinesq equation. We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders, educing the related homotopy series solutions. The convergence region of homotopy series solutions can be adjusted by the auxiliary parameter. Series solutions and similarity reduction equations from approximate symmetry method can be retrieved from approximate homotopy symmetry method. Comment: 17 pages, 4 figures
  03/2009;
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  Available from: ArXiv

  Article: Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

  Xiaoyu Jiao, Ruoxia Yao, S. Y. Lou
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  ABSTRACT: An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations. Comment: 8 pages, 1 figure
  01/2009;
• Source

  Available from: ArXiv

  Article: Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation

  Xiaoyu Jiao, Ruoxia Yao, Shunli Zhang, S. Y. Lou
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  ABSTRACT: For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction equations of different orders enables series reduction solutions. For weak dissipation case, zero-order similarity solutions satisfy the Painlev\'e II, Painlev\'e I and Jacobi elliptic function equations. For weak dispersion case, zero-order similarity solutions are in the form of Kummer, Airy and hyperbolic tangent functions. Higher order similarity solutions can be obtained by solving linear ordinary differential equations.
  02/2008;
• Source

  Available from: sjtu.edu.cn

  Article: Approximate similarity reduction for singularly perturbed Boussinesq equation via symmetry perturbation and direct method

  Xiaoyu Jiao, Ruoxia Yao, S Y Lou
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  ABSTRACT: We investigate the singularly perturbed Boussinesq equation in terms of the ap-proximate symmetry perturbation method and the approximate direct method. The similarity reduction solutions and similarity reduction equations of different orders display formal coincidence for both methods. Series reduction solutions are conse-quently derived. For the approximate symmetry perturbation method, similarity reduction equations of the zero order are equivalent to the Painlevé IV, Painlevé I, and Weierstrass elliptic equations. For the approximate direct method, similarity reduction equations of the zero order are equivalent to the Painlevé IV, Painlevé II, Painlevé I, or Weierstrass elliptic equations. The approximate direct method yields more general approximate similarity reductions than the approximate symmetry perturbation method. © 2008 American Institute of Physics.