Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to n...Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.展开更多
This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the ...This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions （FSSs） and construct some exact FSSs to the resulting equations.展开更多
This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which adm...This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.展开更多
We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to thi...We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.展开更多
We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables...We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.展开更多
The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the pertu...The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.展开更多
文摘Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.
基金The project supported by National Natural Science Foundation of China under Grant No. 10447007 and the Natural Science Foundation of Shaanxi Province of China under Grant No. 2005A13
文摘This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions （FSSs） and construct some exact FSSs to the resulting equations.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10371098, 10447007 and 10475055）, the Natural Science Foundation of Shaanxi Province of China （Grant No 2005A13）.
文摘This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371098 and the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968
文摘We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10371098 and 10447007, the Natural Science Foundation of Shaanxi Province （No 2005A13）, and the Special Research Project of Educational Department of Shaanxi Province （No 03JK060）.
文摘The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.
