非线性双曲型 Schrödinger 方程柯西问题的解析光滑效应

Abstract

Abstract:

In this paper, we study the analytical smoothing effect of Cauchy problem for a class of nonlinear hyperbolic Schrödinger equation. For the Cauchy initial value of exponential decay given in a finite Sobolev space, we prove that the solution of the equation is analytic with respect to both time and space variables when $t\neq0$. Therefore, the hyperbolic Schrödinger equation has analytical smoothing properties similar to the classical Schrödinger equation.

Key words: Cauchy problem, Quasi-differential operator, analytical smoothing effect, hyperbolic Schrödinger equation

CLC Number:

O175.2

Liutao Guo, Chaojiang Xu. Analytical Smoothing Effect on Cauchy Problem of Nonlinear Hyperbolic Schrödinger Equation[J].Acta mathematica scientia,Series A, 2025, 45(5): 1463-1476.

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References

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Analytical Smoothing Effect on Cauchy Problem of Nonlinear Hyperbolic Schrödinger Equation

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