Publications (38)29.32 Total impact
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ABSTRACT: The mixed nonlinear Schr\"odinger (MNLS) equation is a model for the propagation of the Alfv\'en wave in plasmas and the ultrashort light pulse in optical fibers with two nonlinear effects of selfsteepening and self phasemodulation(SPM), which is also the first nontrivial flow of the integrable WadatiKonnoIchikawa(WKI) system. The determinant representation $T_n$ of a nfold Darboux transformation(DT) for the MNLS equation is presented. The smoothness of the solution $q^{[2k]}$ generated by $T_{2k}$ is proved for the two cases ( nondegeneration and doubledegeneration ) through the iteration and determinant representation. Starting from a periodic seed(plane wave), rational solutions with two parameters $a$ and $b$ of the MNLS equation are constructed by the DT and the Taylor expansion. Two parameters denote the contributions of two nonlinear effects in solutions. We show an unusual result: for a given value of $a$, the increasing value of $b$ can damage gradually the localization of the rational solution, by analytical forms and figures. A novel twopeak rational solution with variable height and a nonvanishing boundary is also obtained.07/2014; 
Article: Binary nonlinearization of the nonlinear Schrödinger equation under an implicit symmetry constraint
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ABSTRACT: By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of the nonlinear Schrödinger equation. We show that this system is a completely integrable Hamiltonian system.Acta Mathematicae Applicatae Sinica 06/2014; 30(2). · 0.33 Impact Factor 
Article: Circularly polarized fewcycle optical rogue waves: Rotating reduced MaxwellBloch equations.
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ABSTRACT: The rotating reduced MaxwellBloch (RMB) equations, which describe the propagation of fewcycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from a system of complete MaxwellBloch equations without using the slowly varying envelope approximations. Two hierarchies of the obtained rational solutions, including rogue waves, which are also called fewcycle optical rogue waves, of the rotating RMB equations are constructed explicitly through degenerate Darboux transformation. In addition to the above, the dynamical evolution of the first, second, and thirdorder fewcycle optical rogue waves are constructed with different patterns. For an electric field E in the three lowerorder rogue waves, we find that rogue waves correspond to localized large amplitude oscillations of the polarized electric fields. Further a complementary relationship of two electric field components of rogue waves is discussed in terms of analytical formulas as well as numerical figures.Physical Review E 12/2013; 88(61):062925. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Considering certain terms of the next asymptotic order beyond the nonlinear Schrodinger equation (NLS) equation, the FokasLenells (FL) equation governed by the FL system arise as a model for nonlinear pulse propagation in optical fibers. The expressions of the q[n] and r[n] in the FL system are generated by nfold Darboux transformation (DT). Further, a Taylor series expansion about the norder breather solutions q[n] generated using DT by assuming periodic seed solutions under reduction can generate the norder rogue waves of the FL equation explicitly with 2n+3 free parameters.Mathematical Methods in the Applied Sciences 11/2012; · 0.78 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we construct the additional symmetries of onecomponent constrained discrete KP (cdKP) hierarchy, and then prove that the algebraic structure of the symmetry flows is the positive half of Virasoro algebra.Journal of Mathematical Physics 07/2012; 54(4). · 1.30 Impact Factor 
Article: Surfaces and curves corresponding to the solutions generated from periodic “seed” of NLS equation
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ABSTRACT: The solutions q [n] generated from a periodic “seed” q = cei(as+bt) of the nonlinear Schrödinger (NLS) by nfold Darboux transformation is represented by determinant. Furthermore, the speriodic solution and tperiodic solution are given explicitly by using q [1]. The curves and surfaces (F 1, F 2, F 3) associated with q [n] are given by means of Sym formula. Meanwhile, we show periodic and asymptotic properties of these curves.Acta Mathematica Sinica 01/2012; 28(8). · 0.48 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A new (1+1)dimensional integrable system, i. e. the super coupled Kortewegde Vries (cKdV) system, has been constructed by a super extension of the wellknown (1+1)dimensional cKdV system. For this new system, a novel symmetry constraint between the potential and eigenfunction can be obtained by means of the binary nonlinearization of its Lax pairs. The constraints for even variables are explicit and the constraints for odd variables are implicit. Under the symmetry constraint, the spacial part and the temporal parts of the equations associated with the Lax pairs for the super cKdV system can be decomposed into the super finitedimensional integrable Hamiltonian systems on the supersymmetry manifold $R^{4N2N+2}$, whose integrals of motion are explicitly given. Comment: 12 pages, accepted by Journal of Physics A(2010)Journal of Physics A Mathematical and Theoretical 09/2010; · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction $\{\Phi_i,\Psi_i \}$ are presented explicitly. Furthermore, we show that acting on the space of the wave operator, $\partial_k^*$ forms new centerless $W^{cC}_{1+\infty}$ and $W^{cB}_{1+\infty}$subalgebra of centerless $W_{1+\infty}$ respectively. In order to define above symmetry flows $\partial_k^*$ of the cCKP and cBKP hierarchies, two vital operators $Y_k$ are introduced to revise the additional symmetry flows of the CKP and BKP hierarchies. Comment: 14 pages, accepted by SCIENCE CHINA Mathematics(2010)Science China Mathematics 07/2010; · 0.50 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Based on the AdlerShiotavan Moerbeke (ASvM) formula, the Virasoro constraints and Wconstraints for the preduced qdeformed KadomtsevPetviashvili (qKP) hierarchy are established. Comment: 8 pages, to appear in AIP proceedings, Volume 1212(2010), page 3504/2010;  [Show abstract] [Hide abstract]
ABSTRACT: This paper gives a recursion operator for a 1constrained CKP hierarchy, and by the recursion operator it proves that the 1constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition $q=r$. Comment: To appear in "Acta Matematica Scientia"Acta Mathematica Scientia 04/2010; · 0.49 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the nth flow of the super Dirac hierarchy is decomposed into two super finitedimensional integrable Hamiltonian systems, defined over the supersymmetry manifold R 4N2N with the corresponding dynamical variables x and t n . The integrals of motion required for Liouville integrability are explicitly given. KeywordsSymmetry constraintsBinary nonlinearizationSuper Dirac systemsSuper finitedimensional integrable Hamiltonian systems 2000 MR Subject Classification35Q5137J3537K1037K40Chinese Annals of Mathematics 01/2010; 31(3):361372. · 0.50 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we generalize the Sato theory to the extended bigraded Toda hierarchy (EBTH). We revise the definition of the Lax equations,give the Sato equations, wave operators, Hirota bilinear identities (HBI) and show the existence of $tau$ function $\tau(t)$. Meanwhile we prove the validity of its Faylike identities and Hirota bilinear equations (HBEs) in terms of vertex operators whose coefficients take values in the algebra of differential operators. In contrast with HBEs of the usual integrable system, the current HBEs are equations of product of operators involving $e^{\partial_x}$ and $\tau(t)$. Comment: 29 pages, to appear Journal of Mathematical Physics(2010)Journal of Mathematical Physics 06/2009; · 1.30 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Based on the Lax operator L and OrlovShulman’s M operator, the string equations of the qKP hierarchy are established from the special additional symmetry flows, and the negative Virasoro constraint generators {L −n , n ≥ 1} of the 2reduced qKP hierarchy are also obtained. Keywords qKP hierarchy–Additional symmetry–String equations–Virasoro constraintsChinese Annals of Mathematics 01/2009; 32(6):895904. · 0.50 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A special chain of the gauge transformations of the twocomponent constrained KP is introduced, and then the transformed components and the τfunction of this hierarchy are presented. Based on this, by the different reductions, the gauge transformations of the constrained BKP and the constrained CKP hierarchies are obtained. Furthermore, the transformed component functions and τfunctions of them are expressed by the determinants with the help of the determinant representation of the gauge transformation operators.Journal of Mathematical Physics 11/2007; 48(11):11351911351916. · 1.30 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We establish the binary nonlinearization approach of the spectral problem of the super AKNS system, and then use it to obtain the super finitedimensional integrable Hamiltonian system in supersymmetry manifold $\mathbb{R}^{4N2N}$. The super Hamiltonian forms and integrals of motion are given explicitly. Comment: 13pages, Latex, to appear in Modern Phys. Lett.BModern Physics Letters B 11/2007; · 0.48 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a systematic approach to the construction of soliton solutions for the 5reduction of the Ctype subhierarchy for the Kadomtsev–Petviashvili (CKP) hierarchies starting from the general τfunction τ(n+k) of the Kadomtsev–Petviashvili (KP) hierarchy. We obtain the onesoliton and twosoliton solutions for the bidirectional Kaup–Kupershmidt (bKK) equation, i.e. the 5reduction of CKP hierarchy.Chaos Solitons & Fractals 01/2007; · 1.50 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The nfold Darboux transform (DT) is a 2×2 matrix for the AblowitzKaupNewellSegur (AKNS) system. In this paper, each element of this matrix is expressed by 2n + 1 ranks’ determinants. Using these formulae, the determinant expressions of eigenfunctions generated by the nfold DT are obtained. Furthermore, we give out the explicit forms of the nsoliton surface of the Nonlinear Schrodinger Equation (NLS) by the determinant of eigenfunctions.Science in China Series A Mathematics 12/2006; 49(12):18671878. · 0.70 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a systematic way to construct solutions of the (n=5)reduction of the BKP and CKP hierarchies from the general tau function of the KP hierarchy. We obtain the onesoliton, twosoliton, and periodic solution for the bidirectional SawadaKotera (bSK), the bidirectional KaupKupershmidt (bKK) and also the bidirectional SatsumaHirota (bSH) equation. Different solutions such as left and rightgoing solitons are classified according to the symmetries of the 5th roots of exp(i epsilon). Furthermore, we show that the soliton solutions of the nreduction of the BKP and CKP hierarchies with n= 2 j +1, j=1, 2, 3, ..., can propagate along j directions in the 1+1 spacetime domain. Each such direction corresponds to one symmetric distribution of the nth roots of exp(i epsilon). Based on this classification, we detail the existence of twopeak solitons of the nreduction from the Grammian tau function of the subhierarchies BKP and CKP. If n is even, we again find twopeak solitons. Last, we obtain the "stationary" soliton for the higherorder KP hierarchy.Journal of High Energy Physics 04/2005; · 5.62 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: From the abstract: By using dressing actions of the G n,n1 1,1 system, the authors study geometric transformations for flat timelike nsubmanifolds with flat, nondegenerate normal bundle in antide Sitter space H 1 2n1 (1), where G n1,n1 1,1 =O(2n2,2)/O(n1,1)×O(n1,1).Chinese Annals of Mathematics Series B 01/2005; 3(3).  [Show abstract] [Hide abstract]
ABSTRACT: Infinitesimal deformations of timelike surfaces are investigated in Minkowski 3space ℝ 2,1 . It is shown that some given deformations of the timelike surface can be described by 2+1 dimensional integrable systems. Moreover, spectral parameters are introduced, and it is proved that deformation families are soliton surfaces’ families.Acta Mathematica Scientia 01/2004; 24(4). · 0.49 Impact Factor
Publication Stats
88  Citations  
29.32  Total Impact Points  
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Institutions

1999–2012

University of Science and Technology of China
Luchow, Anhui Sheng, China


2010

Ningbo University
Ningpo, Zhejiang Sheng, China
