Traveling wave solutions have been well studied for various nonlinear systems.However,for high order nonlinear physical models,there still exist various open problems.Here,travelling wave solutions to the well-known f...Traveling wave solutions have been well studied for various nonlinear systems.However,for high order nonlinear physical models,there still exist various open problems.Here,travelling wave solutions to the well-known fifth-order nonlinear physical model,the Sawada–Kotera equation,are revisited.Abundant travelling wave structures including soliton molecules,soliton lattice,kink-antikink molecules,peak-plateau soliton molecules,few-cycle-pulse solitons,double-peaked and triple-peaked solitons are unearthed.展开更多
Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional pa...Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11975131, 11435005 and 11471004)K.C.Wong Magna Fund in Ningbo University
文摘Traveling wave solutions have been well studied for various nonlinear systems.However,for high order nonlinear physical models,there still exist various open problems.Here,travelling wave solutions to the well-known fifth-order nonlinear physical model,the Sawada–Kotera equation,are revisited.Abundant travelling wave structures including soliton molecules,soliton lattice,kink-antikink molecules,peak-plateau soliton molecules,few-cycle-pulse solitons,double-peaked and triple-peaked solitons are unearthed.
基金Supported by National Natural Science Foundation of China under Grant Nos.11071278,111471004the Fundamental Research Funds for the Central Universities of GK201302026 and GK201102007
文摘Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.
