In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic co...In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.展开更多
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on t...We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.展开更多
In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hy...In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.展开更多
基金the National Key Basic Research Project of China under
文摘In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.
基金Project Supported by National Nature Science Foundation of China(10461006)the High Education Science ResearchProgramof Inner Mongolia(NJ02035)the Natural Science Foundation of Inner Mongolia(2004080201103)
文摘We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.
文摘In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.
