The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton soluti...The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.展开更多
A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary f...A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary function of an independent variable.Based on the solution,two hyperbolic functions are chosen to construct new solitons.Novel single-loop-like and double-loop-like solitons are found for the equation.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.10961011 and 60964006
文摘The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.
基金National Natural Science Foundation of China(No.11304409)Nature Science Foundation of Chongqing(No.cstc2018jcyjA0655)Science and Technology Commission Project of Chongqing(No.cstc2017zdcy-zdzxX0011)。
基金The National Nature Science Foundation of China(Nos.61575037,61420021)the China Scholarship Council(No.201606075076)the Innovation Funds of Collaboration Innovation Center of Electronic Materials and Devices(No.ICEM2015-2001)
基金Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education,China (Grant No. KM201010011001),PHR(Grant No. 201106206)the Funding Project for Innovation on Science,Technology and Graduate Education in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality,China (Grant Nos. 201098,PXM2012 014213 000087,PXM2012 014213 000037,and PXM2012 014213 000079)
文摘A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary function of an independent variable.Based on the solution,two hyperbolic functions are chosen to construct new solitons.Novel single-loop-like and double-loop-like solitons are found for the equation.
