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| Non-relativistic Limit from Complex Klein-Gordon Equation to a System of Coupled Nonlinear Schr¨odinger Equations in 2D and 3D |
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Citation： |
Rui JIA ·,Zhibo YANG.Non-relativistic Limit from Complex Klein-Gordon Equation to a System of Coupled Nonlinear Schr¨odinger Equations in 2D and 3D[J].Chinese Annals of Mathematics B,2026,(5):753~770 |
| Page view： 4
Net amount： 4 |
Authors： |
Rui JIA ·; Zhibo YANG |
Foundation： |
the National Natural Science Foundation of China (No. 12171356). |
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| Abstract： |
In this paper, the authors consider the non-relativistic limit of solutions to
the defocusing cubic nonlinear Klein-Gordon equations. Inspired by the work of Lei and
Wu (2023), which considered the real-valued case, the authors show that the solutions to
the complex Klein-Gordon equation can be described by using a system of two coupled
nonlinear Schr¨odinger equations as the speed of light tends to infinity both in two and
three dimensions. On the one hand, if the initial data belong to a lower-regularity Sobolev
space H α, α ∈ [1, 4], the error is proportionate to the α order of the reciprocal of the speed
of light, with a constant that grows linearly in time. On the other hand, if initial data
are smoother (at least in H 4), the error is proportionate to the square of the reciprocal of
the speed of light, with a constant that grows linearly in time. The error of two different
regularity requirements holds globally over time. |
Keywords： |
Nonlinear Klein-Gordon equations Nonlinear Schr¨odinger equations Non-relativistic limit Convergence rate |
Classification： |
35L70, 35Q55, 35B25, 35B40 |
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