Extra-wide-angle parabolic equations in motionless and moving media

Area of Science:

• Physics
• Acoustics
• Computational Mathematics

Background:

• Wide-angle parabolic equations (WAPEs) are crucial in physics for modeling wave propagation.
• Existing WAPEs are typically derived using approximations and solved with finite-difference methods.
• Understanding the physics and applicability of WAPEs is essential for advanced wave modeling.

Purpose of the Study:

• To introduce an extra-wide-angle parabolic equation (EWAPE) as an alternative to traditional WAPEs.
• To develop a novel split-step spectral algorithm for solving the EWAPE.
• To generalize the EWAPE for both small and large variations in refractive index and analyze its applicability.

Main Methods:

• Formulating an extra-wide-angle parabolic equation (EWAPE) in integral form.
• Solving the EWAPE using a perturbation technique and transforming it to the spectral domain.
• Developing a split-step spectral algorithm capable of handling propagation angles up to 90 degrees.

Main Results:

• The proposed EWAPE and its spectral algorithm are valid for small and large refractive index variations.
• All known WAPEs are shown to be special cases of the derived EWAPEs.
• The split-step spectral algorithm simplifies calculations for sound propagation in moving media.

Conclusions:

• The EWAPE provides an alternative derivation and deeper physical insight into WAPEs.
• The developed spectral algorithm offers an innovative and efficient method for wave propagation problems.
• This work enhances the understanding and application range of parabolic equation methods in physics.