A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearize...A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.展开更多
Using the extended homogenous balance method, we obtainabundant exact solution structures ofa (2+1)dimensional integrable model, the generalized Nizhnik-Novikov-Veselov equation. By means of the leading order termanal...Using the extended homogenous balance method, we obtainabundant exact solution structures ofa (2+1)dimensional integrable model, the generalized Nizhnik-Novikov-Veselov equation. By means of the leading order termanalysis, the nonlinear transformations of generalized Nizhnik-Novikov-Veselov equation are given first, and then somespecial types of single solitary wave solution and the multisoliton solutions are constructed.展开更多
Based on homogeneous balance method,soliton solutions to a generalized nonlinear Schrodinger equation (NLSE) with varying coefEcients have been gotten.Our results indicate that a new family of vortex or petal-like spa...Based on homogeneous balance method,soliton solutions to a generalized nonlinear Schrodinger equation (NLSE) with varying coefEcients have been gotten.Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry.It is shown by numerical simulation that these soliton profiles are stable.展开更多
By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential...By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.展开更多
Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear...Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of singlesolitary wave solution and the multisoliton solutions are constructed.展开更多
文摘A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.
文摘Using the extended homogenous balance method, we obtainabundant exact solution structures ofa (2+1)dimensional integrable model, the generalized Nizhnik-Novikov-Veselov equation. By means of the leading order termanalysis, the nonlinear transformations of generalized Nizhnik-Novikov-Veselov equation are given first, and then somespecial types of single solitary wave solution and the multisoliton solutions are constructed.
基金Supported by the Xianning University Foundation of Hubei Province under Grant No.2010CDB05103Xianning University Foundation under Grant No.BK001
文摘Based on homogeneous balance method,soliton solutions to a generalized nonlinear Schrodinger equation (NLSE) with varying coefEcients have been gotten.Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry.It is shown by numerical simulation that these soliton profiles are stable.
基金The project supported by the Natural Science Foundation of Inner Mongolia under Grant No. 200408020113 and National Natural Science Foundation of China under Grant No. 40564001
文摘By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province
文摘Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of singlesolitary wave solution and the multisoliton solutions are constructed.
基金Supported by the Natural Science Foundation of Henan Province of China(0111050200) Natural Science Foundation of Education Committee of Henan Province of China(2003110003)the Science Foundation of Henan University of Science and Technology(2003ZY03)
