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A Necessary and Sufficient Condition for the Solvability of the Nonlinear Schrödinger Equation on a Finite Interval

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Abstract

The admissibility of the initial-boundary data, which characterizes the existence of solution for the initial-boundary value problem, is important. Based on the Fokas method and the inverse scattering transformation, an approach is developed to solve the initial-boundary value problem of the nonlinear Schrödinger equation on a finite interval. A necessary and sufficient condition for the admissibility of the initial-boundary data is given, and the reconstruction of the potential is obtained.

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Authors and Affiliations

  1. Zhengzhou University, Zhengzhou, 450001, China

    Ruo-meng Li & Xian-guo Geng

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  1. Ruo-meng Li
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  2. Xian-guo Geng
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Correspondence to Ruo-meng Li.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11931017 and 11871440), and by the Henan Youth Talent Support Project (Grant No. 2020HYTP001).

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Li, Rm., Geng, Xg. A Necessary and Sufficient Condition for the Solvability of the Nonlinear Schrödinger Equation on a Finite Interval. Acta Math. Appl. Sin. Engl. Ser. 37, 75–100 (2021). https://doi.org/10.1007/s10255-021-0994-z

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  • DOI: https://doi.org/10.1007/s10255-021-0994-z

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