NEW TYPE OF NONISOSPECTRAL KP EQUATION WITH SELF-CONSISTENT SOURCES AND ITS BILINEAR BÄCKLUND TRANSFORMATION

A new type of the nonisospectral KP equation with self-consistent sources is constructed by using the source generation procedure. A new feature of the obtained nonisospectral system is that we allow y-dependence of the arbitrary constants in the determinantal solution for the nonisospectral KP equation. In order to further show integrability of the novel nonisospectral KP equation with self-consistent sources, we give a bilinear Bäcklund transformation.     

INVARIANCE OF THE KAUP–KUPERSHMIDT EQUATION AND TRIANGULAR AUTO-BÄCKLUND TRANSFORMATIONS

We report triangular auto-Bäcklund transformations for the solutions of a fifth-order evolution equation, which is a constraint for an invariance condition of the Kaup–Kupershmidt equation derived by E. G. Reyes in his paper titled "Nonlocal symmetries and the Kaup–Kupershmidt equation" [J. Math. Phys. 46 (2005) 073507, 19 pp.]. These auto-Bäcklund transformations can then be applied to generate solutions of the Kaup–Kupershmidt equation. We show that triangular auto-Bäcklund transformations result from a systematic multipotentialization of the Kupershmidt equation.     

NEW B?CKLUND TRANSFORMATION AND EXACT SOLUTIONS FOR VARIABLE COEFFICIENT KdV EQUATION

In this paper, with the aid of Lax pairs, a new B?cklund transformation for the variable coefficient KdV equation is found, Based on the B?cklund transformation, only if integration is needed, a series of exact solutions can be obtained. This method is important for finding more new and physical-signficant solutions.     

B?CKLUND TRANSFORMAT ION AND CONS ISTEivCE OF REGULAR RIEMANN-HILBERT TRANSFORM

The B?cklund Transformation presented by Chau et al. is reproduced as a self-consistent regular Riemann-Hilbert transform, so that it might correspond to a kind of non-solitonic transformation.     

SOME STATISTICAL PATTERNS OF CHINESE TONE FOR DISYLLABLE AND ITS APPLICATION ON SYNTHESIS OF SPEECH BY RULE

Although the pitch is different in absolute value the pitch contour corresponding to a particularChinese tone should have a similar pattern which is a distinctive feature in speech perception.Thisis an important feature of Chinese language itself. A lot of work on the pitch pattern of Chinese tones has been done,but most of them were onlyqualitative or oversimplified.It is somewhat difficult to apply those results directly to design ofspeech synthesis by rule.This paper has given 15 new statistical results of tone patterns of Chinesedisyllable and each pattern can be formulated simply by a normalized function P(t)in time domainwhich is directly proportional to T_0_(max) and inversely proportional to T_0(t),where T_0_(max) is thereciprocal of the lowest fundamental frequency in the syllable and T_0(t)the pitch period at time t. It has been shown that there are some characteristics in tone pattern of Chinese disyllable: (l) At the beginning and the end of every tone pattern there is always a transient proc     

LAX PAIR,BINARY DARBOUX TRANSFORMATION AND NEW GRAMMIAN SOLUTIONS OF NONISOSPECTRAL KADOMTSEV–PETVIASHVILI EQUATION WITH THE TWO-SINGULAR-MANIFOLD METHOD

In this letter, the two-singular-manifold method is applied to the (2+1)-dimensional nonisospectral Kadomtsev–Petviashvili equation with two Painlevé expansion branches to determine auto-Bäcklund transformation, Lax pairs and Darboux transformation. Based on the two obtained Lax pairs, the binary Darboux transformation is constructed and then the Nth iterated transformation formula in the form of Grammian is also presented. By using these Darboux transformations, we obtain some new grammian solutions.     

SOME DISCUSSIONS ON THE SU(3)×U(1) ELECTRO-WEAK UNIFIED MODEL OF LEPTONS AND QUARKS

In this paper we discussed the following problems in the SU(3)×U(1) unified model proposed earlier: (ⅰ) Two possible choices of the Higgs fields and their comparison with the Weinberg-Salam model; (ⅱ) The form of the Higgs self potential and the realization of the spontaneous symmetry breaking; (ⅲ) The relation between the mass spectrum and the generalized Cabibbo mixing angles in a model with several generations of fermions.