Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonline...Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonlinear excitations such as the algebraic lump-type line solitons, the lumpoff-type half line solitons, and segment solitons.展开更多
For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or ...For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions.展开更多
In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type （1, 0） in the sense of HSrmander and use the atomic decompositions of local Hardy spaces to esta...In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type （1, 0） in the sense of HSrmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.展开更多
In this paper,by introducing the space with weak mixed norms,weak type estimates of two kinds of multilinear fractional Hausdorff operators RΦ,β and SΦ,β on Lebesgue spaces are shown.By virtue of Marcinkiewicz int...In this paper,by introducing the space with weak mixed norms,weak type estimates of two kinds of multilinear fractional Hausdorff operators RΦ,β and SΦ,β on Lebesgue spaces are shown.By virtue of Marcinkiewicz interpolation,strong type estimates of these two operators on Lebesgue spaces are also obtained.Our methods shed some new light on dealing with the case of non-radial function Φ.展开更多
We introduce a class of tri-linear operators that combine features of the bilinear Hilbert transform and paraproduct. For two instances of these operators, we prove boundedness property in alarge range D ={（p1,p2,p3...We introduce a class of tri-linear operators that combine features of the bilinear Hilbert transform and paraproduct. For two instances of these operators, we prove boundedness property in alarge range D ={（p1,p2,p3）ЕR3：1〈p1,p2〈∞,1/p1＋1/p2〈3/2,1〈p3〈∞}展开更多
The(2 + 1)-dimensional Ito equation is extended to a general form including some nonintegrable effects via introducing generalized bilinear operators. It is pointed out that the nonintegrable(2 + 1)-dimensional Ito eq...The(2 + 1)-dimensional Ito equation is extended to a general form including some nonintegrable effects via introducing generalized bilinear operators. It is pointed out that the nonintegrable(2 + 1)-dimensional Ito equation contains lump solutions and interaction solutions between lump and stripe solitons. The result shows that the lump soliton will be swallowed or arisen by a stripe soliton in a fixed time. Furthermore, by the interaction between a lump and a paired resonant stripe soliton, the lump will be transformed to an instanton or a rogue wave.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.11435005Ningbo Natural Science Foundation(No.2015A610159)+1 种基金granted by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzwl1502sponsored by K.C.Wong Magna Fund in Ningbo University
文摘Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonlinear excitations such as the algebraic lump-type line solitons, the lumpoff-type half line solitons, and segment solitons.
基金Supported by the NNSF and the National Education Comittee of China
文摘For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions.
基金supported by National Natural Science Foundation of China(Grant No.10861010)
文摘In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type （1, 0） in the sense of HSrmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201287 and 11201103)a grant of the First-class Discipline of Universities in Shanghai
文摘In this paper,by introducing the space with weak mixed norms,weak type estimates of two kinds of multilinear fractional Hausdorff operators RΦ,β and SΦ,β on Lebesgue spaces are shown.By virtue of Marcinkiewicz interpolation,strong type estimates of these two operators on Lebesgue spaces are also obtained.Our methods shed some new light on dealing with the case of non-radial function Φ.
文摘We introduce a class of tri-linear operators that combine features of the bilinear Hilbert transform and paraproduct. For two instances of these operators, we prove boundedness property in alarge range D ={（p1,p2,p3）ЕR3：1〈p1,p2〈∞,1/p1＋1/p2〈3/2,1〈p3〈∞}
基金Supported by the National Natural Science Foundation of China under Grant No.1143505sponsored by K.C.Wong Magna Fund in Ningbo University
文摘The(2 + 1)-dimensional Ito equation is extended to a general form including some nonintegrable effects via introducing generalized bilinear operators. It is pointed out that the nonintegrable(2 + 1)-dimensional Ito equation contains lump solutions and interaction solutions between lump and stripe solitons. The result shows that the lump soliton will be swallowed or arisen by a stripe soliton in a fixed time. Furthermore, by the interaction between a lump and a paired resonant stripe soliton, the lump will be transformed to an instanton or a rogue wave.
