AUTHOR=Behera Sidheswar 

TITLE=Dynamical solutions and quadratic resonance of nonlinear perturbed Schrödinger equation

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=8

YEAR=2023

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.1086766

DOI=10.3389/fams.2022.1086766

ISSN=2297-4687

ABSTRACT=<p>This work investigates the perturbed nonlinear Schrödinger equation using the modified <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula>-expansion method. The obtained results are generalized and classified into classes of trigonometric, hyperbolic, and rational solutions. The kinematics of soliton and kink profiles are very helpful to understand the propagation of electromagnetic waves inside nonlinear optical fibers. The proposed modified method is unique, straightforward, concise, and effective in the sense that it gives more traveling wave solutions. The findings of this study can strengthen a system's nonlinear dynamic behavior and show how practical the methodology used to attempt to replicate has been. Wolfram Mathematica 11 is used for mathematical simplification and MATLAB is used for graphical simulation.</p>