By using the extended homogeneous balance method, a new auto-Ba^ecklund transformation(BT) to the generalized Kadomtsew-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of the auto...By using the extended homogeneous balance method, a new auto-Ba^ecklund transformation(BT) to the generalized Kadomtsew-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of the auto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations, which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KP equation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results of these equations are also given respectively.展开更多
Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+ 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transforma...Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+ 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.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By using the extended homogeneous balance method, a new auto-Ba^ecklund transformation(BT) to the generalized Kadomtsew-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of the auto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations, which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KP equation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results of these equations are also given respectively.
文摘Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+ 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.
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.
