Through Pickering's and extended Painleve nonstandard truncated expansionmethod, this paper solves the phase-separating dynamics equation of diblock copolymer, and obtainsvarious exact solutions. We discuss non-co...Through Pickering's and extended Painleve nonstandard truncated expansionmethod, this paper solves the phase-separating dynamics equation of diblock copolymer, and obtainsvarious exact solutions. We discuss non-complex special solutions which can be made up of hyperbolicfunctions or elliptic functions.展开更多
Because all the known integrable models possess Schwarzian forms with Moebious transformation invariance,it may be one of the best ways to find new integrable models stating from some suitable Moebious transformation ...Because all the known integrable models possess Schwarzian forms with Moebious transformation invariance,it may be one of the best ways to find new integrable models stating from some suitable Moebious transformation invariant equations.In this paper,we study the Painleve integrability of some special(3+1)-dimensional Schwarzian models.展开更多
The integrability of the coupled, modified KdV equation and the potential Boiti-Leon-Manna-Pempinelli (mKdV-BLMP) system is investigated using the Painlevé analysis approach. It is shown that this coupled system ...The integrability of the coupled, modified KdV equation and the potential Boiti-Leon-Manna-Pempinelli (mKdV-BLMP) system is investigated using the Painlevé analysis approach. It is shown that this coupled system possesses the Painlevé property in both the principal and secondary branches. Then, the consistent Riccati expansion (CRE) method is applied to the coupled mKdV-BLMP system. As a result, it is CRE solvable for the principal branch while non-CRE solvable for the secondary branch. Finally, starting from the last consistent differential equation in the CRE solvable case, soliton, multiple resonant soliton solutions and soliton-cnoidal wave interaction solutions are constructed explicitly.展开更多
This paper investigates a real version of a (2 + 1) dimensional nonlinear Schr?dinger equation through adoption of Painlevé test by means of which the (2 + 1) dimensional nonlinear Schr?dinger equation is studied...This paper investigates a real version of a (2 + 1) dimensional nonlinear Schr?dinger equation through adoption of Painlevé test by means of which the (2 + 1) dimensional nonlinear Schr?dinger equation is studied according to the Weiss et al. method and Kruskal’s simplification algorithms. According to Painlevé test, it is found that the number of arbitrary functions required for explaining the Cauchy-Kovalevskaya theorem exist. Finally, the associated B?cklund transformation and bilinear form is directly obtained from the Painlevé test.展开更多
Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coeffi...Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coefficients. Using the singularity analysis methoddeveloped by J. Weiss and M. D. Kruskal et al. we have proved the sufficient conditionsof the integrabilities and Painleve properties of these two equations. Their Backlund trans-formations and the singularity manifold equations (generalized Schwartz-Boussinesq equationand Schwartz-KdV equation) are obtained. And then these two equations are linearized, i. e.their Lax pairs are given with the time-independent arbitrary spectral parameters includedexplicitly.展开更多
文摘Through Pickering's and extended Painleve nonstandard truncated expansionmethod, this paper solves the phase-separating dynamics equation of diblock copolymer, and obtainsvarious exact solutions. We discuss non-complex special solutions which can be made up of hyperbolicfunctions or elliptic functions.
文摘Because all the known integrable models possess Schwarzian forms with Moebious transformation invariance,it may be one of the best ways to find new integrable models stating from some suitable Moebious transformation invariant equations.In this paper,we study the Painleve integrability of some special(3+1)-dimensional Schwarzian models.
基金Supported by the Natural Science Foundation of Zhejiang Province of China under Grant No LY14A010005
文摘The integrability of the coupled, modified KdV equation and the potential Boiti-Leon-Manna-Pempinelli (mKdV-BLMP) system is investigated using the Painlevé analysis approach. It is shown that this coupled system possesses the Painlevé property in both the principal and secondary branches. Then, the consistent Riccati expansion (CRE) method is applied to the coupled mKdV-BLMP system. As a result, it is CRE solvable for the principal branch while non-CRE solvable for the secondary branch. Finally, starting from the last consistent differential equation in the CRE solvable case, soliton, multiple resonant soliton solutions and soliton-cnoidal wave interaction solutions are constructed explicitly.
基金supported by the National Natural Science Foundation of China(grant No.11371361)the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology(2014)the Key Discipline Construction by China University of Mining and Technology(Grant No.XZD 201602).
文摘This paper investigates a real version of a (2 + 1) dimensional nonlinear Schr?dinger equation through adoption of Painlevé test by means of which the (2 + 1) dimensional nonlinear Schr?dinger equation is studied according to the Weiss et al. method and Kruskal’s simplification algorithms. According to Painlevé test, it is found that the number of arbitrary functions required for explaining the Cauchy-Kovalevskaya theorem exist. Finally, the associated B?cklund transformation and bilinear form is directly obtained from the Painlevé test.
基金Project supported by the National Natural Science Foundation of China.
文摘Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coefficients. Using the singularity analysis methoddeveloped by J. Weiss and M. D. Kruskal et al. we have proved the sufficient conditionsof the integrabilities and Painleve properties of these two equations. Their Backlund trans-formations and the singularity manifold equations (generalized Schwartz-Boussinesq equationand Schwartz-KdV equation) are obtained. And then these two equations are linearized, i. e.their Lax pairs are given with the time-independent arbitrary spectral parameters includedexplicitly.
