MHB Is This Equation Known as the Korteweg-de Vries Equation?

  • Thread starter Thread starter Dustinsfl
  • Start date Start date
  • Tags Tags
    Pde
Click For Summary
The equation presented is indeed known as the Korteweg-de Vries (KdV) equation, which is expressed as ψ_t + ψ_{xxx} + f(ψ)ψ_x = 0. It is significant in the study of shallow water waves and solitons. The KdV equation is a nonlinear partial differential equation that can lead to the nonlinear Schrödinger equation under certain conditions. Its solutions exhibit wave-like behavior, making it crucial in mathematical physics. Understanding the KdV equation is essential for various applications in fluid dynamics and mathematical modeling.
Dustinsfl
Messages
2,217
Reaction score
5
\begin{align*}
\psi_t + \psi_{xxx} + f(\psi)\psi_x &= 0
\end{align*}

This equation leads to the nonlinear Shrodinger equation but does this equation have a name?
 
Physics news on Phys.org

Similar threads

Undergrad Fundamental matrix of a second order 2x2 system of ODEs
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Stuck on solving a non homogenous (linear) PDE
  • · Replies 36 ·
2
Replies
36
Views
5K
Graduate What is the relationship between MHD waves and the Korteweg de Vries equation?
  • · Replies 1 ·
Replies
1
Views
736
Undergrad Explanation of all "its linearly independent derivatives"
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Find the center manifold of a 2D system with double zero eigenvalues
  • · Replies 4 ·
Replies
4
Views
2K
Notes on symmetries of the KdV equation
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Verifying properties of Green's function
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Second order non-homogeneous linear ordinary differential equation
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad PDE - Heat Equation - Cylindrical Coordinates.
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Papapetrou transformation: Conditions to be satisfied to achieve transformation
  • · Replies 1 ·
Replies
1
Views
1K