Initial value problems of cylindrical electromagnetic waves propagation in a nonlinear nondispersive medium

Area of Science:

• Physics
• Electromagnetism
• Wave Propagation

Background:

• Exact solutions for wave propagation problems are crucial.
• Petrov and Kudrin proposed specific initial value conditions for analysis.
• Understanding the impact of nonlinearity on these solutions is essential.

Purpose of the Study:

• To introduce a straightforward method for assessing the accuracy of exact solutions under initial value conditions.
• To evaluate the influence of nonlinearity on initial value problems.
• To establish a criterion for using exact solutions in specific wave propagation scenarios.

Main Methods:

• Development of a simple estimation technique for solution accuracy.
• Comparative analysis of linear and nonlinear cases for initial value conditions.
• Focus on cylindrical electromagnetic wave propagation in a nonlinear, nondispersive medium.

Main Results:

• The proposed method effectively estimates solution accuracy.
• A notable difference in initial value conditions between linear and nonlinear cases was observed, even with weak nonlinearity.
• The findings highlight the importance of considering nonlinearity.

Conclusions:

• The developed method serves as a reliable criterion for employing exact solutions.
• It is particularly relevant for initial value problems involving cylindrical electromagnetic waves in nonlinear media.
• Accurate analysis requires careful consideration of nonlinear effects on initial conditions.