This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation,iut—uxx+i(|u|4u)x=0,x eT.The existence of a large amount of quasi-periodic solutions with two frequencies for this equati...This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation,iut—uxx+i(|u|4u)x=0,x eT.The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established.The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem.We mention that in the present paper the mean value of u does not need to be zero,but small enough,which is different from the assumption(1.7)in Geng-Wu[J.Math.Phys.、53,102702(2012)].展开更多
In this paper, by the Aubry-Mather theory, it is proved that there are many periodic solutions and usual or generalized quasiperiodic solutions for relativistic oscillator with anharmonic potentials models d/dt（x/√1...In this paper, by the Aubry-Mather theory, it is proved that there are many periodic solutions and usual or generalized quasiperiodic solutions for relativistic oscillator with anharmonic potentials models d/dt（x/√1-｜x｜2）＋｜x｜^α-1x=p（t）,where p（t） ∈ C0（R1） is 1-periodic and α 〉 0.展开更多
基金Supported by NSFC(Grant Nos.11601487 and 11526189)
文摘This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation,iut—uxx+i(|u|4u)x=0,x eT.The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established.The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem.We mention that in the present paper the mean value of u does not need to be zero,but small enough,which is different from the assumption(1.7)in Geng-Wu[J.Math.Phys.、53,102702(2012)].
基金Supported by the NNSF(Grant No.11371132)Key Laboratory of High Performance Computing and Stochastic Information Processing
文摘In this paper, by the Aubry-Mather theory, it is proved that there are many periodic solutions and usual or generalized quasiperiodic solutions for relativistic oscillator with anharmonic potentials models d/dt（x/√1-｜x｜2）＋｜x｜^α-1x=p（t）,where p（t） ∈ C0（R1） is 1-periodic and α 〉 0.
