On nonlinearity parameter in Nonlinear Schrodinger Equation (NLS)

Click For Summary
SUMMARY

The discussion centers on the Nonlinear Schrödinger (NLS) equation and its application in wave propagation in fluids, specifically regarding the nonlinearity parameter, N, which is observed to be significantly high (N≈O(10^4)). The validity of the weak nonlinearity assumption is questioned when N is much greater than one (N>>1). The referenced paper by A.H. Nayfeh discusses nonlinear wave packet propagation in a hard-walled circular duct, providing foundational insights into the topic.

PREREQUISITES
  • Understanding of the Nonlinear Schrödinger (NLS) equation
  • Familiarity with wave propagation in fluid dynamics
  • Knowledge of nonlinearity parameters in mathematical modeling
  • Basic principles of acoustics as related to wave behavior
NEXT STEPS
  • Research the implications of high nonlinearity parameters in the NLS equation
  • Study the weak nonlinearity assumption in fluid dynamics
  • Explore advanced applications of the NLS equation in acoustics
  • Review A.H. Nayfeh's paper on nonlinear wave packet propagation for deeper insights
USEFUL FOR

Researchers in fluid dynamics, physicists studying wave phenomena, and mathematicians focusing on nonlinear equations will benefit from this discussion.

vijay0
Messages
3
Reaction score
0
While I am studying the wave propagation in fluids, the amplitude modulation seems to be governed by the Nonlinear Schrödinger (NLS) equation. In some of the journal papers the nonlinearity parameter, N seems to be of high value (N≈O(104)) and so on. I understand that weak nonlinearity assumption is used in the paper. With N>>1 is the weak nonlinearity assumption valid?

Paper: A.H. Nayfeh. "Nonlinear propagation of a wave packet in a hard‐walled circular duct." The Journal of the Acoustical Society of America 57.4 (1975): 803-809.
 
Physics news on Phys.org
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

Similar threads

Undergrad Can Nonlinear Equations be Linearized Using Free Parameters?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate The Nonlinear Schrödinger Equation
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Schrödinger's original interpretation
  • · Replies 21 ·
Replies
21
Views
4K
Graduate Dieter Zeh's MWI as Schrödinger equation + further assumptions
  • · Replies 27 ·
Replies
27
Views
4K
Graduate Wave Packet: What is It & What Does NLS Say?
  • · Replies 5 ·
Replies
5
Views
10K
Graduate The eigenvalue power method for quantum problems
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Slow variables in Nonlinear Schrodinger Equation
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Spacetime Engineering by Superposition of GWs: Feasible in Theory?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Twistors and celestial holography
  • · Replies 21 ·
Replies
21
Views
7K
Admissions Exploring the Universe: Pursuing a PhD in High Energy Physics
  • · Replies 8 ·
Replies
8
Views
4K