Quasi-periodic Solutions for One-Dimensional Nonlinear Lattice Schrödinger Equation with Tangent Potential
نویسندگان
چکیده
In this paper, we construct time quasi-periodic solutions for the nonlinear lattice Schrödinger equation iq̇n + (qn+1 + qn−1) + tanπ(nα̃+ x)qn + |qn|qn = 0, n ∈ Z, where α̃ satisfies a certain Diophantine condition and x ∈ R/Z. We prove that for sufficiently small, the equation admits a family of small-amplitude time quasi-periodic solutions for “most” of x belonging to R/Z.
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ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 45 شماره
صفحات -
تاریخ انتشار 2013