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We study the Cauchy problem of the nonlinear fourth-order Schrödinger equation with gain or loss: \(iu_{t}+\triangle^{2}u+\lambda|u|^{\alpha}u +i\varepsilon a(t)|u|^{\beta}u=0\), \(x\in R^{n}\), \(t\in R\), where \(2\leq\alpha\leq\frac{8}{n-4}\) and \(2\leq\beta\leq\frac{8}{n-4}\), ε is a real number, \(a(t)\) is a real function, and \(n>4\). We study the asymptotic properties of its local and global solutions as \(\varepsilon\rightarrow0\).

The asymptotic property for nonlinear fourth-order Schrödinger equation with gain or loss