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Linear and Nonlinear Waves
MATH 6940
Spring 2026
Yuri V. Lvov
lvovy@rpi.edu x6893
Monday 2pm-4pm
Office Hours : Mondays, 18:00-20:00, webex personal room
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Lecture Notes
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Lecture Notes
First Lecture
Step 1: Separation of variables
Step 2: Solve the spatial part
Step 3: Solve the temporal part
Step 4: General solution
Step 5: Fourier sine coefficients
Summary
Second Lecture - perturbation Theory and Mode Coupling
Selection rules for the triple–sine overlap integral.
Selection rules for the four–sine overlap integral.
Fourier transform:
Beams
FPUT Hamiltonian lecture
Real-space Hamiltonian
Discrete Fourier Transform
Quadratic Hamiltonian in Fourier Space
Cubic Hamiltonian in Fourier Space
Canonical Transformation to Normal Variables
Cubic Hamiltonian in Normal Variables
Home Works
First Home work
Second Home work
Home Work Three
Fourier Tranform
1. Hamilton's Equations in Real Space
2. Discrete Fourier Transform
3. Chain Rule for Fourier-Space Derivatives
4. Fourier-Space Hamilton's Equations
5. Comments
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lvovy@rpi.edu x6893
