An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explic...An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.展开更多
基金Supported by the Natural Science Foundation of China under the grant 11026165 and 11072053Doctaral Fund of Ministry of Education of China under the grant 20100041120037the Fundamental Research Funds for the Central Universities
文摘An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.
