The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,...The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.展开更多
With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dpˉ-operators in term of the Hirota direct method ...With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dpˉ-operators in term of the Hirota direct method when the appropriate value of pˉ is determined. Furthermore, the resulting approach is applied to solve the extended(2+1)-dimensional Shallow Water Wave equation, and the periodic wave solution is obtained and reduced to soliton solution via asymptotic analysis.展开更多
Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any str...Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in B as their substrings.From the fact that a string in the language is equivalent to a path in the corresponding graph,we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.展开更多
基金Supported by the GUCAS President Grant,the National Natural Science Foundation of China under Grant No.10701076
文摘The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.
基金Supported by Shandong Provincial Key Laboratory of Marine Ecology and Environment&Disaster Prevention and Mitigation project under Grant No.2012010National Natural Science Foundation of China under Grant No.11271007+1 种基金Special Funds for Theoretical Physics of the National Natural Science Foundation of China under Grant No.11447205Shandong University of Science and Technology Research Fund under Grant No.2012KYTD105
文摘With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dpˉ-operators in term of the Hirota direct method when the appropriate value of pˉ is determined. Furthermore, the resulting approach is applied to solve the extended(2+1)-dimensional Shallow Water Wave equation, and the periodic wave solution is obtained and reduced to soliton solution via asymptotic analysis.
基金This research is supported by the National Natural Science Foundation of China (No. 10271103) Natural Science Foundation of Yunnan Province(No. 2003F0015M).
文摘Given an alphabet ∑ and a finite minimal set B of forbidden words,a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in B as their substrings.From the fact that a string in the language is equivalent to a path in the corresponding graph,we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.
