Abstract: In this course, we will use the Korteweg-de Vries
equation as a model to understand the behavior of dispersive
partial differential equations. Through this lens, we will discuss
dispersion, well-posedness, and solitons. We will also...
Abstract: Fourier series are classically used to construct
solutions to partial differential equations such as the wave and
Schrödinger equations. In Fourier restriction theory, additional
conditions are imposed on the frequencies of these series...
Abstract: How do we check if two vectors are orthogonal? We
compute their dot product, which by definition takes two vectors as
inputs. How do we check if two functions are orthogonal? We compute
their inner product, which by definition takes two...
Abstract: In this course, we will use the Korteweg-de Vries
equation as a model to understand the behavior of dispersive
partial differential equations. Through this lens, we will discuss
dispersion, well-posedness, and solitons. We will also...
Abstract: Fourier series are classically used to construct
solutions to partial differential equations such as the wave and
Schrödinger equations. In Fourier restriction theory, additional
conditions are imposed on the frequencies of these series...
Abstract: In this course, we will use the Korteweg-de Vries
equation as a model to understand the behavior of dispersive
partial differential equations. Through this lens, we will discuss
dispersion, well-posedness, and solitons. We will also...
Abstract: Fourier series are classically used to construct
solutions to partial differential equations such as the wave and
Schrödinger equations. In Fourier restriction theory, additional
conditions are imposed on the frequencies of these series...
Abstract: In this course, we will use the Korteweg-de Vries
equation as a model to understand the behavior of dispersive
partial differential equations. Through this lens, we will discuss
dispersion, well-posedness, and solitons. We will also...
Abstract: Fourier series are classically used to construct
solutions to partial differential equations such as the wave and
Schrödinger equations. In Fourier restriction theory, additional
conditions are imposed on the frequencies of these series...