Looking at a solitary initial state

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SUMMARY

The discussion centers on analyzing the deformation of a solitary initial state defined by the equation u0(x) = a0x²(1-x)² for 0 ≤ x ≤ 1 and u0(x) = 0 for x > 1. It is established that deformation does not occur if the constant c remains unchanged. Participants emphasize the need for a differential equation and additional context to provide meaningful guidance on methods for visualizing the deformation over time, including producing video frames.

PREREQUISITES
  • Understanding of solitary wave solutions in partial differential equations
  • Familiarity with initial value problems in mathematical physics
  • Knowledge of numerical methods for solving differential equations
  • Experience with video frame generation techniques for visualizing mathematical phenomena
NEXT STEPS
  • Research methods for solving nonlinear partial differential equations, such as the Korteweg-de Vries equation
  • Learn about numerical simulation techniques, specifically finite difference methods
  • Explore software tools for visualizing mathematical functions, such as MATLAB or Python's Matplotlib
  • Investigate techniques for generating video frames from mathematical simulations, including rendering options in Python or MATLAB
USEFUL FOR

Mathematicians, physicists, and engineers interested in the dynamics of solitary waves, as well as educators and students seeking to visualize complex mathematical concepts through simulation.

simo1
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I have this equation

u0(x) = a0x2(1-x)2 for 0≤ x ≤ 1
= 0 for x>1
i have to investigate how will a solitary initial state such as the one above deform as time goes on.

I know it will not deform if c is constant. when they say I must do this by a well-lnown method and produce video frmaes, could you suggest which methods to use
 
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We need a lot more context to help you out, I think.

1. Where is the differential equation? All I see here is a function definition.

2. In what context does this differential equation arise? Can you give us the initial problem?

3. What is $c$?
 

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