In this paper, based on sinh-cosh method and sinh-Gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.These solutions include Jacobi elliptic function solution, soliton solution,trigonometric function solution.

We first recall some basic definitions and facts about Jacobi manifolds, generalized Lie bialgebroids, generalized Courant algebroids and Dirac structures. We establish an one-one correspondence between reducible Dirac structures of the generalized Lie bialgebroid of a Jacobi manifold (M,Λ, E) for which 1 is an admissible function and Jacobi quotient manifolds of M . We study Jacobi reductions ...

A generalization of the cyclic Jacobi algorithm is proposed that works in an arbitrary compact Lie algebra. This allows, in particular, a unified treatment of Jacobi algorithms on different classes of matrices, such as, e.g., skew-symmetric or skew-Hermitian Hamiltonian matrices. Wildberger has established global, linear convergence of the algorithm for the classical Jacobi method on compact Li...

From the classical differential equation of Jacobi fields, one naturally defines the Jacobi operator of a Riemannian manifold with respect to any tangent vector. A straightforward computation shows that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute. In this way, we classify the real hypersurfaces in quaternionic projective spaces all of whose tange...

We introduce an orthogonal system on the half line, induced by Jacobi polynomials. Some results on the Jacobi rational approximation are established, which play important roles in designing and analyzing the Jacobi rational spectral method for various differential equations, with the coefficients degenerating at certain points and growing up at infinity. The Jacobi rational spectral method is p...

The Jacobi algorithm for eigenvalue calculation of symmetric matrices can be performed with a CORDIC algorithm as its basic module. Recently, a simpliied Jacobi algorithm, by employing approximate rotations based on CORDIC rotations, was proposed. It fully exploits the binary data structure and reduces the overall computational cost signiicantly. In this paper an error analysis of the approxima...

Jacobi sets have been identified as significant in multi-field topological analysis, but are defined in the domain of the data rather than in the Reeb Space. This distinction is significant, as exploiting multi-field topology actually depends on the projection of the Jacobi set into the Reeb Space, and the details of its internal structure. We therefore introduce the Jacobi Structure of a Reeb ...

We analyze the relationship between the covering of the Jacobi group and the squeezed states. We attach some nonclassical states to the Jacobi group. The matrix elements of the Jacobi group are presented.

Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrix r new rows and columns, so that the original Jacobi matrix is shifted downward. The r new...

In this paper we give extensions of the mass formula for biweight enumerators and the Jacobi weight enumerators of binary self-dual codes and binary doubly even self-dual codes. For binary doubly even self-dual codes, our formula is expressed in terms of the root system E8 embedded in C4 for biweight enumerators, while the root system D4 is employed for Jacobi weight enumerators. For self-dual ...