Algebraic Lower Bounds on the Spatial Analyticity Radius for Higher Order Nonlinear Schrödinger Equations

Tegegne Getachew, Birilew Belayneh and Betre Shiferaw

Journal of Applied Mathematics, 2025, vol. 2025, 1-10

Abstract: We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈℠,ux,0=u0x, where j≥2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℠and has a uniform radius of spatial analyticity σ0 in the space variable. For such initial data, we prove that the initial value problem is locally well-posed using space-time estimates and show that the radius of spatial analyticity of the solution remains σ0 till some lifespan 0 0 is a constant. Our proof relies on standard contraction mapping argument, Plancherel’s Theorem, Hölder’s inequality, space-time Strichartz estimates for the free Schrödinger equation, energy estimate and one-dimensional Sobolev embedding.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:9997857

DOI: 10.1155/jama/9997857

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