Based on computerized symbolic computation and a new general ansatz,an extended Riccati equation rational expansion method is presented to construct multiple exact solutions for nonlinear evolution equations and implemented in a computer algebraic system.The validity and reliability of the method are tested by its application to four nonlinear evolution equations arising in physics,namely,gener...

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...

We consider one of the fundamental problems classical invariant theory - research Hilbert polynomials for algebra invariants Lie group S L 2 . Form gives us important information about structure algebra. Besides, coefficients and degree polynomial play an role in Algebraic Geometry. It is well-known that function n -invariants quasi-polynomial. The Cayley-Sylvester formula calculation values co...

We establish the nonlinear stability of $N$-soliton solutions modified Korteweg-de Vries (mKdV) equation. The are global mKdV behaving at (positive and negative) time infinity as sums $1$-solitons with speeds $0<c_1<\cdots< c_N$.The proof relies on variational characterization $N$-solitons. show that $N$-solitons realize local minimum $(N+1)$-th conserved quantity subject to fixed constraints $...

Recently, recursive blocked algorithms for solving triangular one-sided and two-sided Sylvester-type equations were introduced by Jonsson and K̊agström. This elegant yet simple technique enables an automatic variable blocking that has the potential of matching the memory hierarchies of today’s HPC systems. The main parts of the computations are performed as level 3 general matrix multiply and ad...

We introduce the concept of Stieltjes integral of an operator-valued function with respect to the spectral measure associated with a normal operator. We give sufficient conditions for the existence of this integral and find bounds on its norm. The results obtained are applied to the Sylvester and Riccati operator equations. Assuming that the entry C is a normal operator, the spectrum of the ent...

For N-coupled generalized time-dependent oscillators, primary invariants and a generalized invariant are found in terms of classical solutions. Exact quantum motions satisfying the Heisenberg equation of motion are also found. For number states and coherent states of the generalized invariant, the uncertainties in positions and momenta are obtained.

In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ; g2, g3)(g2, g3, invariants) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid ...