In this paper, we give a coupled lattice equation with the help of Hirota operators, which comes from a special BKP lattice. Two-soliton and three-soliton solutions to the coupled system are constructed. Furthermore,r...In this paper, we give a coupled lattice equation with the help of Hirota operators, which comes from a special BKP lattice. Two-soliton and three-soliton solutions to the coupled system are constructed. Furthermore,resonant interaction of the two-soliton solution is analyzed in detail. Under some special resonant condition, it is shown that low soliton can propagate faster than high one. Finally, the N-soliton solution is presented in the Pfaffian form.展开更多
The generalized inverse function-valued Padé approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, t...The generalized inverse function-valued Padé approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, to simplify computation of the function-valued Padé approximants, an efficient Pfaffian formula for the determinants was extended from the matrix form to the function-valued form. As an important application, a Pfaffian formula of [4/4] type Padé approximant was established.展开更多
In ihis paper.an instability problem of an unsteady oscillationo flow is studied.In particultar,the phase.function of the disturbance wave.system is soived by using the charocteristic theory of partial differential eq...In ihis paper.an instability problem of an unsteady oscillationo flow is studied.In particultar,the phase.function of the disturbance wave.system is soived by using the charocteristic theory of partial differential equation and an expansion of Orysommerfeid eigenvalue problem.instead of using the disturbance model which is given previously The.flow considered is a combination of plane Poiseuille.flow with aflow oscillating periodically and its instability is found for a special initial value of a developing wave due to continuous oscillationg source.展开更多
This paper constructs more general exact solutions than N-soliton solution and Wronskian solution for variable- coefficient Kadomtsev-Petviashvili （KP） equation. By using the Hirota method and Pfaffian technique, it...This paper constructs more general exact solutions than N-soliton solution and Wronskian solution for variable- coefficient Kadomtsev-Petviashvili （KP） equation. By using the Hirota method and Pfaffian technique, it finds the Grammian determinant-type solution for the variable-coefficient KP equation （VCKP）, the Wronski-type Pfaffian solution and the Gram-type Pfaffian solutions for the Pfaffianized VCKP equation.展开更多
The (2 + 1)-dimensional Korteweg de Vries (KdV) equation, which was first derived by Boiti et al., has been studied by various distinct methods. It is known that this (2 + 1)-dimensional KdV equation has rich solution...The (2 + 1)-dimensional Korteweg de Vries (KdV) equation, which was first derived by Boiti et al., has been studied by various distinct methods. It is known that this (2 + 1)-dimensional KdV equation has rich solutions, such as multi-soliton solutions and dromion solutions. In the present article, a unified representation of its N-soliton solution is given by means of pfaffian. We’ll show that this (2 + 1)-dimensional KdV equation is nothing but the Plücker identity when its τ-function is given by pfaffian.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11371251,11301331 and 10971136supported by Innovation Program of Shanghai Municipal Education Commission under Grant No.14YZ135Young Teacher Training Program of Shanghai Universities,Shanghai 085 Project and Tian-Yuan Fund for Mathematics under Grant No.11226194
文摘In this paper, we give a coupled lattice equation with the help of Hirota operators, which comes from a special BKP lattice. Two-soliton and three-soliton solutions to the coupled system are constructed. Furthermore,resonant interaction of the two-soliton solution is analyzed in detail. Under some special resonant condition, it is shown that low soliton can propagate faster than high one. Finally, the N-soliton solution is presented in the Pfaffian form.
文摘The generalized inverse function-valued Padé approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, to simplify computation of the function-valued Padé approximants, an efficient Pfaffian formula for the determinants was extended from the matrix form to the function-valued form. As an important application, a Pfaffian formula of [4/4] type Padé approximant was established.
文摘In ihis paper.an instability problem of an unsteady oscillationo flow is studied.In particultar,the phase.function of the disturbance wave.system is soived by using the charocteristic theory of partial differential equation and an expansion of Orysommerfeid eigenvalue problem.instead of using the disturbance model which is given previously The.flow considered is a combination of plane Poiseuille.flow with aflow oscillating periodically and its instability is found for a special initial value of a developing wave due to continuous oscillationg source.
基金Project supported by the National Key Basic Research Project of China （2004CB318000）, the National Science Foundation of China （Grant No 10371023） and Shanghai Shuguang Project of China （Grant No 02SG02）.
文摘This paper constructs more general exact solutions than N-soliton solution and Wronskian solution for variable- coefficient Kadomtsev-Petviashvili （KP） equation. By using the Hirota method and Pfaffian technique, it finds the Grammian determinant-type solution for the variable-coefficient KP equation （VCKP）, the Wronski-type Pfaffian solution and the Gram-type Pfaffian solutions for the Pfaffianized VCKP equation.
文摘The (2 + 1)-dimensional Korteweg de Vries (KdV) equation, which was first derived by Boiti et al., has been studied by various distinct methods. It is known that this (2 + 1)-dimensional KdV equation has rich solutions, such as multi-soliton solutions and dromion solutions. In the present article, a unified representation of its N-soliton solution is given by means of pfaffian. We’ll show that this (2 + 1)-dimensional KdV equation is nothing but the Plücker identity when its τ-function is given by pfaffian.
