Exact solution of paraxial wave dynamical model with Kerr Media by using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e1344"><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msup></mml:math> model expansion technique
Hamood Ur Rehman, Aziz Ullah Awan, Seham Ayesh Allahyani, Sayed M. Eldin, Muhammad Ahsan Binyamin, Sadia Yasin
Abstract
This paper discusses optical soliton solutions for the paraxial wave model (PWM) in Kerr law media. Mathematically, the PWM for a monochromatic beam is equivalent to the Schrödinger equation of free quantum particle. The ϕ6 model expansion technique is used to obtain dark, bright, singular, bright-dark combined and periodic solitons. The solutions obtained by this method are in the form of trigonometric, hyperbolic, and exponential functions. To prompt the important propagated structures, some scrutinized solutions are demonstrated in the form of 3D, contour, and 2D plots using specific values to the parameters with constrained conditions. It is observed that this method is an efficient, secure, and stable tool for new precise solitons for various NLPDEs in engineering and applied sciences.