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FOUR
UTLES DE
NAA
IER NANNALESS
LIN TITDELINSTITUT FOURIER
JeanMarc DELORT
Semiclassical microlocal normal forms and global solutions of modified
onedimensional KG equations
Tome 66, no 4 (2016),
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How to fill out semiclassical microlocal normal forms

How to fill out semiclassical microlocal normal forms
01
Identify the principal symbol of the given operator.
02
Expand the symbol into its Taylor series around a given point.
03
Apply a series of transformations to make the leading term diagonal and eliminate the lower order terms.
04
Normalize the resulting symbol to a canonical form by using suitable linear symplectic transformations.
Who needs semiclassical microlocal normal forms?
01
Researchers in the field of microlocal analysis and semiclassical analysis.
02
Physicists working on the quantization of classical systems.
03
Mathematicians studying pseudodifferential operators and Fourier integral operators.
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What is semiclassical microlocal normal forms?
Semiclassical microlocal normal forms are mathematical tools used in the study of partial differential equations and wave phenomena, providing a framework to analyze the behavior of solutions in a semiclassical context.
Who is required to file semiclassical microlocal normal forms?
Typically, researchers and mathematicians working in the field of applied mathematics or theoretical physics may need to file or adopt semiclassical microlocal normal forms in their studies.
How to fill out semiclassical microlocal normal forms?
Filling out semiclassical microlocal normal forms involves applying the appropriate mathematical techniques and transformations to represent the problem at hand in the correct form, often requiring a thorough understanding of the underlying physics and mathematics.
What is the purpose of semiclassical microlocal normal forms?
The purpose of semiclassical microlocal normal forms is to simplify the analysis of differential equations by providing a clearer picture of the singularities and propagation of waves, ultimately aiding in understanding complex systems.
What information must be reported on semiclassical microlocal normal forms?
Typically, information such as the type of differential equations involved, boundary conditions, singularities, and the asymptotic behavior of solutions must be reported when using semiclassical microlocal normal forms.
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