Numerically solving NLS equation

  • Context: Graduate 
  • Thread starter Thread starter hanson
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on using the Split Step Fourier Method to numerically solve the Nonlinear Schrödinger (NLS) equation, specifically in the context of water waves. The user successfully created an animation of soliton collisions based on the exact solution but encountered discrepancies when comparing it to the numerical solution. Despite refining the step size, the numerical results did not align with the expected profiles during interactions. The NLS equation in question is expressed as iut + uxx + |u|^2u = 0.

PREREQUISITES
  • Understanding of the Nonlinear Schrödinger (NLS) equation
  • Familiarity with the Split Step Fourier Method
  • Knowledge of numerical analysis techniques
  • Basic concepts of soliton theory in fluid dynamics
NEXT STEPS
  • Research advanced techniques for improving numerical stability in the Split Step Fourier Method
  • Explore the impact of different step sizes on numerical solutions of the NLS equation
  • Investigate alternative numerical methods for solving the NLS equation, such as the Crank-Nicolson method
  • Find and analyze existing animations of NLS soliton collisions to compare methodologies
USEFUL FOR

Researchers and practitioners in applied mathematics, physicists studying fluid dynamics, and anyone interested in numerical methods for solving nonlinear partial differential equations.

hanson
Messages
312
Reaction score
0
Hi all.
I am using the Split Step Fourier Method to solve NLS to study the interaction of two solitons.
I have done the animation of the collision of two solitons for exact solution.

But when I numerically solve it and watch the animation, the profiles during interaction is not quite the same. I don't really know what's wrong. I have used a finer step size to try again. But it doesn't help.

Will the numerical solution resemble the exact solution very well during interaction?

Can you kindly refer me to some animations of NLS soliton collision using numerical solutions? I am using the NLS in water wave context in the most simple form, namely iut+uxx+u^2u=0.
 
Physics news on Phys.org
hanson said:
iut+uxx+u^2u=0.
It going to be
iut + uxx + |u|^2u = 0
 

Similar threads

Graduate Why Do Simulated and Theoretical Soliton Collisions Differ?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate How to solve simple 2D space-time PDE numerically
  • · Replies 5 ·
Replies
5
Views
3K
Graduate How to Implement Constant C in the Split Step Fourier Method for NLS Equations?
  • · Replies 1 ·
Replies
1
Views
8K
Graduate Solve PDE w/ Comsol 5.3: Numerical Solution & Time Evolution
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Nonlinear Wave Equation (Nonlinear Helmholtz)
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad The algorithms involved in finding a solution with numerical methods
  • · Replies 14 ·
Replies
14
Views
3K
Graduate Partial differential equation containing the Inverse Laplacian Operator
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Few more numerical methods question....?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Numerical solution of non-linear diffusion equation
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Numerical solution to Schrödinger equation - eigenvalues
  • · Replies 1 ·
Replies
1
Views
3K