Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP equations

By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are taken as an illustrative example: new modified KP equations with $m$ arbitrary time-dependent coefficients are obtained possessing symmetries involving $m$ arbitrary functions of time. A particular graded symmetry algebra for the modified KP equations is derived in this connection homomorphic to the Virasoro algebras.Comment: 19 pages, latex, to appear in J. Nonlinear Math. Phy

On integrability of a (2+1)-dimensional perturbed Kdv equation

A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlev\'e test for integrability well, and its 4$\times$4 Lax pair with two spectral parameters is found. The results show that the Painlev\'e classification of coupled KdV equations by A. Karasu should be revised

Integrable Theory of the Perturbation Equations

An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries, linear representations (Lax and zero curvature representations) and Hamiltonian structures etc. and provides us a method to generate hereditary operators, Hamiltonian operators and symplectic operators starting from the known ones. The resulting perturbation equations give rise to a sort of integrable coupling of soliton equations. Two examples (MKdV hierarchy and KP equation) are carefully carried out.Comment: 27 pages, latex, to appear in Chaos, Soliton & Fractal

Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation

Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\"acklund transformations of the linear form and some special cases are considered.Comment: 14pages, Latex, to appear in Intern. J. Nonlinear Mechanics, the original latex file is not complet

A three-by-three matrix spectral problem for AKNS hierarchy and its binary Nonlinearization

A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess classical Hamiltonian structures, in which the nonlinearized spatial system is intimately related to stationary AKNS flows. These nonlinearized Lax systems also lead to a sort of involutive solutions to each AKNS soliton equation.Comment: 21pages, in Late

Coupled KdV equations of Hirota-Satsuma type

It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlev\'e test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown

A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

Q2Q^2--Dependence of the Gerasimov-Drell-Hearn Sum Rule

We test the Gerasimov-Drell-Hearn (GDH) sum rule numerically by calculating the total photon absorption cross sections $\sigma_{1/2}$ and $\sigma_{3/2}$ on the nucleon via photon excitation of baryon resonances in the constituent quark model. A total of seventeen, low-lying, non-strange baryon resonances are included in this calculation. The transverse and longitudinal interference cross section, $\sigma_{1/2}^{TL}$, is found to play an important role in the study of the $Q^2$ variation of the sum rule. The results show that the GDH sum rule is saturated by these resonances at a confidence level of 94%. In particular, the $P_{33}(1232)$ excitation largely saturates the sum rule at $Q^2 = 0$, and dominates at small $Q^2$. The GDH integral has a strong $Q^2$-dependence below $Q^2= 1.0 {GeV}^2$ and changes its sign around $Q^2= 0.3 {GeV}^2$. It becomes weakly $Q^2$-dependent for $Q^2 > 1.0 {GeV}^2$ because of the quick decline of the resonance contributions. We point out that the $Q^2$ variation of the GDH sum rule is very important for understanding the nucleon spin structure in the non-perturbative QCD region.Comment: revtex, 17 pages, 3 ps figs include

Photo-production of Nucleon Resonances and Nucleon Spin Structure Function in the Resonance Region

The photo-production of nucleon resonances is calculated based on a chiral constituent quark model including both relativistic corrections H{rel} and two-body exchange currents, and it is shown that these effects play an important role. We also calculate the first moment of the nucleon spin structure function g1 (x,Q^2) in the resonance region, and obtain a sign-changing point around Q^2 ~ 0.27 {GeV}^2 for the proton.Comment: 23 pages, 5 figure

Measurements of J/psi Decays into 2(pi+pi-)eta and 3(pi+pi-)eta

Based on a sample of 5.8X 10^7 J/psi events taken with the BESII detector, the branching fractions of J/psi--> 2(pi+pi-)eta and J/psi-->3(pi+pi-)eta are measured for the first time to be (2.26+-0.08+-0.27)X10^{-3} and (7.24+-0.96+-1.11)X10^{-4}, respectively.Comment: 11 pages, 6 figure