As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivativ...As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this paper.By application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are obtained.At the same time,the similarity reductions are derived.Furthermore,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional derivative.By virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential operators.By using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are derived.Finally,the traveling wave solutions are achieved and plotted.展开更多
We study the Cauchy problem for the Davey–Stewartson equation i?tu+Δu+|u|^(2) u+E1(|u|^(2))u=0,(t,x)∈R×R^(3).The dichotomy between scattering and finite time blow-up shall be proved for initial data with finit...We study the Cauchy problem for the Davey–Stewartson equation i?tu+Δu+|u|^(2) u+E1(|u|^(2))u=0,(t,x)∈R×R^(3).The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u0)E(u0)above the ground state threshold M(Q)E(Q).展开更多
基金the National Natural Science Foundation of China(Grant No.11975143)。
文摘As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this paper.By application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are obtained.At the same time,the similarity reductions are derived.Furthermore,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional derivative.By virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential operators.By using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are derived.Finally,the traveling wave solutions are achieved and plotted.
基金supported by the National Natural Science Foundation of China(11361069)the Natural Science Foundation of Educational Department of Yunnan Province(2013Y482)
基金Supported by the Natural Science Foundation of China (10471059)the Natural Science Foundation of Anhui Province(070416225)+1 种基金the Natural Science Foundation of Anhui Education Bureau(KJ2007A003)the Faculty Fund of Anhui University
基金Supported by Natural Science Foundation of China(Grant Nos.11501111,11771082 and 11601082)China Scholarship Council(Grant No.201808350018)Foundation of the Science and Technology Department of Fujian Province(Grant No.2017J05002)。
文摘We study the Cauchy problem for the Davey–Stewartson equation i?tu+Δu+|u|^(2) u+E1(|u|^(2))u=0,(t,x)∈R×R^(3).The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u0)E(u0)above the ground state threshold M(Q)E(Q).
