Gelombang Non Linier

Tahun Akademik:
Genap 2022/2023
Kelas-Offr:
P1-P1
Deskripsi:

Introduction: 1.1 Linear waves, 1.1.1 Sinusoidal waves, 1.1.2 The wave equation, 1.1.3 Dispersion, 1.2 Nonlinear waves, 1.3 Solitons. 2 The Fourier transform: 2.1 The Schwartz space,
2.2 The Fourier transform on S, 2.3 Extension of the Fourier transform to Lp. 3 Linear PDE with constant coefficients: 3.1 The heat equation, 3.1.1 Derivation, 3.1.2 Solution by Fourier’s method,
3.1.3 The heat kernel, 3.1.4 Qualitative properties, 3.2 The wave equation, 3.2.1 Derivation, 3.2.2 Solution by Fourier’s method, 3.2.3 Solution formulas, 3.2.4 Qualitative properties, 3.3 The Laplace equation, 3.4 General PDE and the classification of second order equations, 3.5 Well-posedness of the Cauchy problem, 3.6 Hyperbolic operators. 4 First order quasilinear equations: 4.1 Some definitions, 4.2 The method of characteristics, 4.3 Conservation laws, 4.3.1 Discontinuous solutions, 4.3.2 The Riemann problem, 4.3.3 Entropy conditions. 5 Distributions and Sobolev spaces: 5.1 Distributions, 5.2 Operations on distributions, 5.3 Tempered distributions, 5.4 Approximation with smooth functions, 5.5 Sobolev spaces. 6 Dispersive equations: 6.1 Calculus in Banach spaces, 6.2 NLS, 6.2.1 Linear theory, 6.2.2 Nonlinear theory, 6.3 KdV, 6.3.1 Linear theory, 6.3.2 Nonlinear theory, 6.3.3 Derivation of the KdV equation, 6.4 Further reading. 7 Solitons and complete integrability: 7.1 Miura’s transformation, Gardner’s extension and infinitely many conservation laws, 7.2 Soliton solutions, 7.3 Lax pairs, 7.3.1 The scattering problem, 7.3.2 The evolution equation, 7.3.3 The relation to Lax pairs, 7.3.4 A Lax-pair formulation for the KdV equation.


Capaian Pembelajaran

  • Melalui kerja Proyek I, peserta menunjukkan konsep-konsep teoritis dan prinsip-prinsip bidang khusus fisika; mampu mendiseminasikan hasil kajian masalah dan perilaku fisis dalam bentuk lisan, tulisan, dan visual sesuai kaidah ilmiah baku yang bebas plagiasi; mampu menunjukkan kinerja mandiri, bermutu, dan terukur.

  • Melalui kerja Proyek II, peserta menunjukkan konsep-konsep teoritis dan prinsip-prinsip bidang khusus fisika; mampu mendiseminasikan hasil kajian masalah dan perilaku fisis dalam bentuk lisan, tulisan, dan visual sesuai kaidah ilmiah baku yang bebas plagiasi; mampu menunjukkan kinerja mandiri, bermutu, dan terukur.

Daftar Pustaka:

  • Erik Wahlén, 2011, An Introduction to Nonlinear Waves.