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

MHB
Thread starter Dustinsfl
Start date Sep 3, 2013
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Pde

In summary, a PDE (partial differential equation) is a mathematical equation involving partial derivatives of an unknown function of multiple independent variables. It is different from an ODE (ordinary differential equation) in that it can involve multiple variables. PDEs are commonly used in physics, engineering, and economics to model various phenomena, such as heat flow, wave propagation, and electrostatics. There is no general method for solving all types of PDEs, and different techniques are used depending on the type of equation. PDEs are used in a wide range of real-world applications, including heat transfer, fluid dynamics, population dynamics, and many others. They are also used in research areas such as climate modeling and financial forecasting.

Sep 3, 2013

Dustinsfl

\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?

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Sep 3, 2013

Ackbach

Gold Member

MHB

It's the Korteweg-de Vries equation.

Related to Is This Equation Known as the Korteweg-de Vries Equation?

1. What is a PDE?

A PDE, or partial differential equation, is a mathematical equation that involves partial derivatives of an unknown function of several independent variables. It is commonly used to model physical phenomena in fields such as physics, engineering, and economics.

2. How is a PDE different from an ordinary differential equation (ODE)?

An ODE involves only ordinary derivatives of an unknown function, while a PDE involves partial derivatives. This means that a PDE can involve multiple independent variables, while an ODE only involves one.

3. What are some examples of PDEs?

Some common examples of PDEs include the heat equation, wave equation, and Laplace's equation. These equations are used to model phenomena such as heat flow, wave propagation, and electrostatics, respectively.

4. How are PDEs solved?

There is no general method for solving all types of PDEs. Different types of PDEs require different techniques, such as separation of variables, Fourier transforms, or numerical methods. In some cases, PDEs can also be solved using computer software.

5. What real-world applications use PDEs?

PDEs are used in a wide range of fields, including physics, engineering, economics, and biology. They are used to model phenomena such as heat transfer, fluid dynamics, population dynamics, and many more. PDEs are also used in many areas of research, such as climate modeling and financial forecasting.