In this paper, we consider the following coupled Schrodinger system with χ^(2) nonlinearities {-Δu1+V1(x)u1=αu1u2,x∈R^N,-Δu2+V2(x)u2=α/2u^21+βu^22,x∈R^N.which arises from second-harmonic generation in quadrati...In this paper, we consider the following coupled Schrodinger system with χ^(2) nonlinearities {-Δu1+V1(x)u1=αu1u2,x∈R^N,-Δu2+V2(x)u2=α/2u^21+βu^22,x∈R^N.which arises from second-harmonic generation in quadratic media. Here V1(x) and V2(x) are radially positive functions, 2 ≤ N < 6, α > 0 and α > β. Assume that the potential functions V1(x) and V2(x) satisfy some algebraic decay at infinity. Applying the finite dimensional reduction method, we construct an unbounded sequence of non-radial vector solutions of synchronized type.展开更多
基金partially supported by NSFC(11671162,11601194)CCNU18CXTD04 and CZQ13017。
文摘In this paper, we consider the following coupled Schrodinger system with χ^(2) nonlinearities {-Δu1+V1(x)u1=αu1u2,x∈R^N,-Δu2+V2(x)u2=α/2u^21+βu^22,x∈R^N.which arises from second-harmonic generation in quadratic media. Here V1(x) and V2(x) are radially positive functions, 2 ≤ N < 6, α > 0 and α > β. Assume that the potential functions V1(x) and V2(x) satisfy some algebraic decay at infinity. Applying the finite dimensional reduction method, we construct an unbounded sequence of non-radial vector solutions of synchronized type.
