A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic functio...A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained.展开更多
The generalized Riccati equation vational expansion method is extended in this paper. Several exact solutions for the generalized Burgers-Fisher equation with variable coefficients are obtained by this method, and som...The generalized Riccati equation vational expansion method is extended in this paper. Several exact solutions for the generalized Burgers-Fisher equation with variable coefficients are obtained by this method, and some of which are derived for the first time. It is concluded from the results that this approach is simple and efficient even in solving partial differential equations with variable coefficients.展开更多
Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soli...Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.展开更多
In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with thr...In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.展开更多
PU （phase unwrapping） is the key step and important problem in DEM （digital elevation model） extraction and the measurement of surface deformation of InSAR （Interferometric synthetic aperture radar）. The CKFPUA ...PU （phase unwrapping） is the key step and important problem in DEM （digital elevation model） extraction and the measurement of surface deformation of InSAR （Interferometric synthetic aperture radar）. The CKFPUA （conventional Kalman filter phase unwrapping algorithm） can obtain reliable results in the flat terrain areas, but it caused error transmission not making the accurate inversion of surface deformation information in the steep terrain. Considering this situation, so it needs to introduce topographic information for guiding phase unwrapping. Here the 90 m resolution DEM data have been used and it is obtained by SRTM （shuttle radar topography mission） measured jointly by NASA （National Aeronautics and Space Administration） and NIMA （National Imaging Mapping Agency） of U.S. Department of Defense. This paper presents a SD-KFPUA （Kalman filter phase unwrapping algorithm） based on SRTM DEM. With SRTM DEM directing InSAR image to implement phase unwrapping, the speed and accuracy are improved. By analyzing with the conventional Kalman filter phase unwrapping algorithms, it is shown that the proposed method can achieve good results in particular to improve unwrapping accuracy in the low coherence region.展开更多
In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in...In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in Bose-Einstein condensates are obtained.展开更多
In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in line...In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained.展开更多
In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presen...In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.展开更多
Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not ...Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacob/elliptic functions. The results also show that if the arbitrary constants are selected suitably, the approximate solutions may become the exact ones.展开更多
Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic pot...Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.展开更多
We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization ...We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).展开更多
Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solu...Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solutions,solitoff-typed solutions are obtained. With the help of the truncated Painlev′e expansion, the corresponding nonlocal symmetry is also given, and furthermore, the nonlocal symmetry is localized by prolonging the related enlarged system.展开更多
The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explici...The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.展开更多
基金supported by National Natural Science Foundation of China under Grant No. 10205007the National Natural Science Foundation Gansu Province of China under Grant No. 3zS041-A25-011
文摘A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained.
基金Supported by the National Basic Research Project of China (973 Program No. 2006CB705500)by the National Natural Science Foundation of China under Grant Nos. 10975216, 10635040by the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20093402110032
文摘The generalized Riccati equation vational expansion method is extended in this paper. Several exact solutions for the generalized Burgers-Fisher equation with variable coefficients are obtained by this method, and some of which are derived for the first time. It is concluded from the results that this approach is simple and efficient even in solving partial differential equations with variable coefficients.
文摘Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.J50101Key Disciplines of Shanghai Municipality under Grant No.S30104
文摘In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.
基金Acknowledgments The research is supported by the National Science Foundation of China （40874001） and National 863 plans projects of China （2009AA12Z147）. The authors would like to express thanks to ESA （European Space Agency） for providing ENVISAT satellite data.
文摘PU （phase unwrapping） is the key step and important problem in DEM （digital elevation model） extraction and the measurement of surface deformation of InSAR （Interferometric synthetic aperture radar）. The CKFPUA （conventional Kalman filter phase unwrapping algorithm） can obtain reliable results in the flat terrain areas, but it caused error transmission not making the accurate inversion of surface deformation information in the steep terrain. Considering this situation, so it needs to introduce topographic information for guiding phase unwrapping. Here the 90 m resolution DEM data have been used and it is obtained by SRTM （shuttle radar topography mission） measured jointly by NASA （National Aeronautics and Space Administration） and NIMA （National Imaging Mapping Agency） of U.S. Department of Defense. This paper presents a SD-KFPUA （Kalman filter phase unwrapping algorithm） based on SRTM DEM. With SRTM DEM directing InSAR image to implement phase unwrapping, the speed and accuracy are improved. By analyzing with the conventional Kalman filter phase unwrapping algorithms, it is shown that the proposed method can achieve good results in particular to improve unwrapping accuracy in the low coherence region.
基金Supported by National Natural Science Foundation of China under Grant No. 90511009
文摘In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in Bose-Einstein condensates are obtained.
基金Supported by National Natural Science Foundation of China under Grant No.90511009
文摘In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained.
基金supported by the research grant under the Government of Malaysia
文摘In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.
基金Supported by National Natural Science Foundation of China under Grant No.11104248Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ12A01008Project of Education of Zhejiang Province under Grant No.Y201327716
文摘Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacob/elliptic functions. The results also show that if the arbitrary constants are selected suitably, the approximate solutions may become the exact ones.
基金Supported by National Natural Science Foundation of China under Grant Nos.11375030 and 61304133
文摘Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.
基金supported by National Natural Science Foundation of China(Grant No.11401595)
文摘We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).
基金Supported by the National Natural Science Foundation of China under Grant Nos.11405103,11571008,51679132,11601321,and 11526137
文摘Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solutions,solitoff-typed solutions are obtained. With the help of the truncated Painlev′e expansion, the corresponding nonlocal symmetry is also given, and furthermore, the nonlocal symmetry is localized by prolonging the related enlarged system.
基金Supported by the National Natural Science Foundation of Zhejiang Province under Grant No.LZ15A050001the National Natural Science Foundation of China under Grant No.11675146
文摘The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.
