The following coupled Schrodinger system with a small perturbationis considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and...The following coupled Schrodinger system with a small perturbationis considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution （called the generalized heteroclinic solution thereafter）.展开更多
We study a generalized Frenkel-Kontorova model and obtain periodic and heteroclinic mountain pass solutions.The heteroclinic mountain pass solution in the second laminations is new to the generalized Frenkel-Kontorova...We study a generalized Frenkel-Kontorova model and obtain periodic and heteroclinic mountain pass solutions.The heteroclinic mountain pass solution in the second laminations is new to the generalized Frenkel-Kontorova model.Our proof follows that of Bolotin and Rabinowitz(2005)for an Allen-Cahn equation,which is different from the heat flow method of finding the critical point of the Frenkel-Kontorova model in the literature.The proofs depend on suitable choices of functionals and working spaces.We also study the multiplicity of these mountain pass solutions.展开更多
A class of lattice with time delay and nonlocal response is considered.By transforming the lattice delay differential system into an integral equations in a Banach space,we reduces a singular perturbation problem to a...A class of lattice with time delay and nonlocal response is considered.By transforming the lattice delay differential system into an integral equations in a Banach space,we reduces a singular perturbation problem to a regular perturbation problem.Traveling wave solution therefore is obtained by applying Liapunov-Schmidt method and the implicit function theorem.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11126292,11201239,11371314)the Guangdong Natural Science Foundation(No.S2013010015957)the Project of Department of Education of Guangdong Province(No.2012KJCX0074)
文摘The following coupled Schrodinger system with a small perturbationis considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution （called the generalized heteroclinic solution thereafter）.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.34000-31610274)。
文摘We study a generalized Frenkel-Kontorova model and obtain periodic and heteroclinic mountain pass solutions.The heteroclinic mountain pass solution in the second laminations is new to the generalized Frenkel-Kontorova model.Our proof follows that of Bolotin and Rabinowitz(2005)for an Allen-Cahn equation,which is different from the heat flow method of finding the critical point of the Frenkel-Kontorova model in the literature.The proofs depend on suitable choices of functionals and working spaces.We also study the multiplicity of these mountain pass solutions.
文摘A class of lattice with time delay and nonlocal response is considered.By transforming the lattice delay differential system into an integral equations in a Banach space,we reduces a singular perturbation problem to a regular perturbation problem.Traveling wave solution therefore is obtained by applying Liapunov-Schmidt method and the implicit function theorem.
