In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations....In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.展开更多
A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficien...A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficient KdV equation under an external forcing isderived for large amplitude equatorial Rossby wave in a shear How. And then various periodic-likestructures for these equatorial Rossby waves are obtained with the help of Jacobi ellipticfunctions. It is shown that the external forcing plays an important role in various periodic-likestructures.展开更多
By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other ...By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.展开更多
In this paper, we study higher order elliptic partial differential equations with variable growth, and obtain the existence of solutions in the setting of Wm,p（x） spaces by means of an abstract result for variationa...In this paper, we study higher order elliptic partial differential equations with variable growth, and obtain the existence of solutions in the setting of Wm,p（x） spaces by means of an abstract result for variational inequalities obtained by Gossez and Mustonen. Our result generalizes the corresponding one of Kováik and Rákosník.展开更多
The present work is devoted to the bending problems of prismatic shell with the thickness vanishing at infinity as an exponential function. The bending equation in the zero approximation of Vekua＇s hierarchical model...The present work is devoted to the bending problems of prismatic shell with the thickness vanishing at infinity as an exponential function. The bending equation in the zero approximation of Vekua＇s hierarchical models is considered. The problem is reduced to the Dirichlet boundary value problem for elliptic type partial differential equations on half-plane. The solution of the problem under consideration is constructed in the integral form.展开更多
The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct m...The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.展开更多
Following work carried out earlier on linear-quadratic optimal control for linear finitedimensional stationary systems we report,in this article,on extension of some of those results to certaininfinite dimensional sys...Following work carried out earlier on linear-quadratic optimal control for linear finitedimensional stationary systems we report,in this article,on extension of some of those results to certaininfinite dimensional systems;in particular a class of PDE systems of elliptic type.These systems arestudied in the now familiar framework developed by J.L.Lions and E.Magenes,specialized to asubclass of such systems important in a variety of applications.As an extended example this paperstudies an optimal redistribution problem in a groundwater flow system governed by Darcy's equation,presenting both analytic and computational work related to such problems.展开更多
The authors show the regularity of weak solutions for some typical quasi-linear elliptic systems governed by two p-Laplacian operators. The weak solutions of the following problem with lack of compactness are proved t...The authors show the regularity of weak solutions for some typical quasi-linear elliptic systems governed by two p-Laplacian operators. The weak solutions of the following problem with lack of compactness are proved to be regular when α(x) and α,β,p, q satisfy some conditions: where Ω (?) RN (N≥3) is a smooth bounded domain.展开更多
To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d w...To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper approximations.As applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.展开更多
文摘In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
文摘A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficient KdV equation under an external forcing isderived for large amplitude equatorial Rossby wave in a shear How. And then various periodic-likestructures for these equatorial Rossby waves are obtained with the help of Jacobi ellipticfunctions. It is shown that the external forcing plays an important role in various periodic-likestructures.
基金Supported by the Natural Science Foundation of Education Committee of Henan Province(2003110003)Supported by the Natural Science Foundation of Henan Province(0111050200)
文摘By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.
文摘In this paper, we study higher order elliptic partial differential equations with variable growth, and obtain the existence of solutions in the setting of Wm,p（x） spaces by means of an abstract result for variational inequalities obtained by Gossez and Mustonen. Our result generalizes the corresponding one of Kováik and Rákosník.
文摘The present work is devoted to the bending problems of prismatic shell with the thickness vanishing at infinity as an exponential function. The bending equation in the zero approximation of Vekua＇s hierarchical models is considered. The problem is reduced to the Dirichlet boundary value problem for elliptic type partial differential equations on half-plane. The solution of the problem under consideration is constructed in the integral form.
文摘The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.
文摘Following work carried out earlier on linear-quadratic optimal control for linear finitedimensional stationary systems we report,in this article,on extension of some of those results to certaininfinite dimensional systems;in particular a class of PDE systems of elliptic type.These systems arestudied in the now familiar framework developed by J.L.Lions and E.Magenes,specialized to asubclass of such systems important in a variety of applications.As an extended example this paperstudies an optimal redistribution problem in a groundwater flow system governed by Darcy's equation,presenting both analytic and computational work related to such problems.
基金Project supported by the National Natural Science Foundation of China (No.10271077).
文摘The authors show the regularity of weak solutions for some typical quasi-linear elliptic systems governed by two p-Laplacian operators. The weak solutions of the following problem with lack of compactness are proved to be regular when α(x) and α,β,p, q satisfy some conditions: where Ω (?) RN (N≥3) is a smooth bounded domain.
基金supported by National Natural Science Foundation of China(Grant Nos.10971059,11071265 and 11171232)the Funds for Creative Research Groups of China(Grant No.11021101)+2 种基金the National Basic Research Program of China(Grant No.2011CB309703)the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciencesthe Program for Innovation Research in Central University of Finance and Economics
文摘To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper approximations.As applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.
