This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solito...This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solitons propagating against a Painlevé wave background,in analogy to the established notion of elliptic solitons,which refers to solitons on an elliptic wave background.By employing a novel symmetry decomposition method aided by nonlocal residual symmetries,we explicitly construct (extended) Painlevé Ⅱ solitons for the Korteweg-de Vries equation and (extended) Painlevé Ⅳ solitons for the Boussinesq equation.展开更多
文章研究含变系数的广义浅水波(generalized shallow water wave)方程,该方程是对浅水波方程的一种推广,在物理学等领域具有更广泛的应用.首先使用WTC法检测该方程的Painlevé可积性,并利用Painlevé截断法构造自Bäcklund...文章研究含变系数的广义浅水波(generalized shallow water wave)方程,该方程是对浅水波方程的一种推广,在物理学等领域具有更广泛的应用.首先使用WTC法检测该方程的Painlevé可积性,并利用Painlevé截断法构造自Bäcklund变换,进而导出一系列新的解析解.同时使用李对称分析法求得无穷小生成子与李对称群,对该系统的相似约化方程、守恒律进行研究.展开更多
This paper focuses on the analytical technique based on nonlocal symmetry and consistent tanh expansion method for constructing abundant analytical solutions of a new extended Kadomtsev-Petviashvili-Benjamin-Ono(eKP-B...This paper focuses on the analytical technique based on nonlocal symmetry and consistent tanh expansion method for constructing abundant analytical solutions of a new extended Kadomtsev-Petviashvili-Benjamin-Ono(eKP-BO)equation in(2+1)dimensions.First,commencing with the Painlevéanalysis,the integrability of the(2+1)-dimensional eKP-BO equation and its nonlocal symmetry are discussed.Second,the localization of the nonlocal symmetry of the extended system is determined by means of the prolongation method.Furthermore,through this localization process,the initial value problem of the extended system is solved,thereby providing a finite symmetry transformation of the(2+1)-dimensional eKP-BO equation.Finally,we follow the consistent tanh expansion method to unveil the interaction solutions of the solitoncnoidal type and resonant soliton type to the eKP-BO equation,and we study their dynamic properties in a visual manner.展开更多
基金supported by the National Natural Science Foundations of China (Grant Nos.12235007,12001424,12271324,and 12501333)the Natural Science Basic research program of Shaanxi Province (Grant Nos.2021JZ-21 and 2024JC-YBQN-0069)+3 种基金the China Postdoctoral Science Foundation (Grant Nos.2020M673332 and 2024M751921)the Fundamental Research Funds for the Central Universities (Grant No.GK202304028)the 2023 Shaanxi Province Postdoctoral Research Project (Grant No.2023BSHEDZZ186)Xi’an University,Xi’an Science and Technology Plan Wutongshu Technology Transfer Action Innovation Team(Grant No.25WTZD07)。
文摘This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solitons propagating against a Painlevé wave background,in analogy to the established notion of elliptic solitons,which refers to solitons on an elliptic wave background.By employing a novel symmetry decomposition method aided by nonlocal residual symmetries,we explicitly construct (extended) Painlevé Ⅱ solitons for the Korteweg-de Vries equation and (extended) Painlevé Ⅳ solitons for the Boussinesq equation.
文摘文章研究含变系数的广义浅水波(generalized shallow water wave)方程,该方程是对浅水波方程的一种推广,在物理学等领域具有更广泛的应用.首先使用WTC法检测该方程的Painlevé可积性,并利用Painlevé截断法构造自Bäcklund变换,进而导出一系列新的解析解.同时使用李对称分析法求得无穷小生成子与李对称群,对该系统的相似约化方程、守恒律进行研究.
基金the National Natural Science Foundation of China(Grant Nos.11835011,12375006 and 12074343).
文摘This paper focuses on the analytical technique based on nonlocal symmetry and consistent tanh expansion method for constructing abundant analytical solutions of a new extended Kadomtsev-Petviashvili-Benjamin-Ono(eKP-BO)equation in(2+1)dimensions.First,commencing with the Painlevéanalysis,the integrability of the(2+1)-dimensional eKP-BO equation and its nonlocal symmetry are discussed.Second,the localization of the nonlocal symmetry of the extended system is determined by means of the prolongation method.Furthermore,through this localization process,the initial value problem of the extended system is solved,thereby providing a finite symmetry transformation of the(2+1)-dimensional eKP-BO equation.Finally,we follow the consistent tanh expansion method to unveil the interaction solutions of the solitoncnoidal type and resonant soliton type to the eKP-BO equation,and we study their dynamic properties in a visual manner.
基金Supported by National Science Foundation of China ( Grant No. 60973146)National Science Foundation of Shandong Province,China(Grant No. 2R2009GM036)Foundation for Study Encouragement to Middel-aged and Young Scientists of Shandong Province,China(Grant No.2008BS01019)
