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
Under the Flaschka-Newell Lax pair,the Darboux transformation for the Painlevé-Ⅱequation is constructed by the limiting technique.With the aid of the Darboux transformation,the rational solutions are represented...Under the Flaschka-Newell Lax pair,the Darboux transformation for the Painlevé-Ⅱequation is constructed by the limiting technique.With the aid of the Darboux transformation,the rational solutions are represented by the Gram determinant,and then we give the large y asymptotics of the determinant and the rational solutions.Finally,the solution of the corresponding Riemann-Hilbert problem is obtained from the Darboux matrices.展开更多
We focused on the two-coupled Maccari's system.With the help of truncated Painlevéapproach(TPA),we express local solution in the form of arbitrary functions.From the solution obtained,using its appropriate ar...We focused on the two-coupled Maccari's system.With the help of truncated Painlevéapproach(TPA),we express local solution in the form of arbitrary functions.From the solution obtained,using its appropriate arbitrary functions,we have generated the rogue wave pattern solutions,rogue wave solutions,and lump solutions.In addition,by controlling the values of the parameters in the solutions,we show the dynamic behaviors of the rogue wave pattern solutions,rogue wave solutions,and lump solutions with the aid of Maple tool.The results of this study will contribute to the understanding of nonlinear wave dynamics in higher dimensional Maccari's systems.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Project supported by the National Natural Science Foundation of China (Grant No.12101246)。
文摘Under the Flaschka-Newell Lax pair,the Darboux transformation for the Painlevé-Ⅱequation is constructed by the limiting technique.With the aid of the Darboux transformation,the rational solutions are represented by the Gram determinant,and then we give the large y asymptotics of the determinant and the rational solutions.Finally,the solution of the corresponding Riemann-Hilbert problem is obtained from the Darboux matrices.
文摘We focused on the two-coupled Maccari's system.With the help of truncated Painlevéapproach(TPA),we express local solution in the form of arbitrary functions.From the solution obtained,using its appropriate arbitrary functions,we have generated the rogue wave pattern solutions,rogue wave solutions,and lump solutions.In addition,by controlling the values of the parameters in the solutions,we show the dynamic behaviors of the rogue wave pattern solutions,rogue wave solutions,and lump solutions with the aid of Maple tool.The results of this study will contribute to the understanding of nonlinear wave dynamics in higher dimensional Maccari's systems.
