# Questions tagged [dispersive-pde]

This tag is for questions relating to dispersive partial differential equation or dispersive PDE. Informally, “dispersion” will refer to the fact that different frequencies in this equation will tend to propagate at different velocities, thus dispersing the solution over time.

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### Estimates of kernel function of Schrodinger Operator concerning Littlewood Paley projection operator

Maybe this problem is difficult to understand, because we lump integration and distribution together(usually we can distinguish them). I have some trouble about the following proof concerning the ...
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### Describing terms of a PDE

I have seen words like 'dispersive', 'advective' and 'diffusive' when describing certain terms in PDEs - however I am unsure on the exact intuition behind this terminology and how one is to know how a ...
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### Relating a dispersion equation to an eigenvalue equation in a Fourier transformed system of PDEs

I am reading through the paper "Dynamics of Membranes Driven by Actin Polymerization" by Nir S. Gov and Ajay Gopinathan. In it a set of coupled differential equations for a mathematical ...
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### How to find the relation between $\omega$ and $\kappa$?

Suppose we have a system of equations: \begin{gather*} \left(\begin{array}{cccc} c\partial_t +\partial_x & \alpha & 0 &0 \\ N_0 & \partial_t & -\sigma_2 \frac{Q_0}{N_0} & \...
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### Why is the solution of the periodic KdV equation unique?

Bourgain proved that the periodic KdV equation \begin{align} \partial_t u+\partial_x^3 u+u\partial_x u&=0\\u(0,x)&=u_0(x)\end{align} is locally well-posed in $H^s(\mathbb T)$ in [1]. Here ...
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### Non-Schwartz functions in Bourgain space X^{s,b}?

From Terence Tao's Nonlinear dispersive equations: local and global analysis, Definition 2.7: The Bourgain space $X^{s,b}(\mathbb R\times\mathbb R^n)$ is defined to be the closure of the set of ...
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### Wave equation: predicting geometric dispersion with group theory

Context The wave equation $$\partial_{tt}\psi=v^2\nabla^2 \psi$$ describes waves that travel with frequency-independent speed $v$, ie. the waves are dispersionless. The character of solutions is ...
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