The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and math...The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.展开更多
Applying the Lie group method to the differential-difference equation,the Lie point symmetry of Blaszak-Marciniakfour-field Lattice equation is obtained.Using the obtained symmetry,the similarity reduction equationsof...Applying the Lie group method to the differential-difference equation,the Lie point symmetry of Blaszak-Marciniakfour-field Lattice equation is obtained.Using the obtained symmetry,the similarity reduction equationsof Blaszak-Marciniak four-field Lattice equation are derived.Solving the reduction,we get the solution of Blaszak-Marciniakfour-held Lattice equation which not only recovers one of the solutions obtained by Ma and Hu [J.Math.Phys.40 (1999) 6071] but also has the singularity when we choose the arbitrary constants accurately.展开更多
基金Project supported by the National Key Basic Research Project of China (Grant No 2004CB318000)the National Natural Science Foundation of China (Grant Nos 10771072 and 10735030)Shanghai Leading Academic Discipline Project of China (Grant No B412)
文摘The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.
基金Supported by the National Natural Science Foundation of China under Grant No.10735030the National Natural Science Foundation of China under Grant No.90718041+1 种基金Shanghai Leading Academic Discipline Project under Grant No.B412Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT0734
文摘Applying the Lie group method to the differential-difference equation,the Lie point symmetry of Blaszak-Marciniakfour-field Lattice equation is obtained.Using the obtained symmetry,the similarity reduction equationsof Blaszak-Marciniak four-field Lattice equation are derived.Solving the reduction,we get the solution of Blaszak-Marciniakfour-held Lattice equation which not only recovers one of the solutions obtained by Ma and Hu [J.Math.Phys.40 (1999) 6071] but also has the singularity when we choose the arbitrary constants accurately.
