Optical solitons of the Nonlinear Schrödinger Equation with a parametric order of non linearity: Exact analytical solutions

Optical solitons of the Nonlinear Schrödinger Equation with a parametric order of non linearity: Exact analytical solutions | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 10 December 2025 V1 Latest version Share on Optical solitons of the Nonlinear Schrödinger Equation with a parametric order of non linearity: Exact analytical solutions Authors : Djouakoua Tcheumanak Franck-Djimitri , Nicodème Djiedeu 0000-0001-6961-2222 [email protected] , Wembe Tafo Evariste , Jean Pierre Nguenang , and Tchawoua Clement Authors Info & Affiliations https://doi.org/10.22541/au.176535020.05719919/v1 158 views 194 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract A theoretical study leading to analytical solutions of the nonlinear Schrödinger equation with a parametric order of non linearity is reported in this work. Looking for travelling waves solutions, the nonlinear Schrödinger equation was transformed and separated into real and imaginary parts. One of the two differential equations allows us to derive the wave’s group velocity. Using this group velocity the relationship between the group and the phase velocities was established. This relationship is in agreement with a property of left-handed metamaterials. Using the relation of dispersion we deduced the phase velocity. The other differential equation allowed to determine the amplitudes of the waves. For a zero constant of integration, we obtained three types of solutions: two couples of hyperbolic solutions and a couple of trigonometric solutions. The wave’s line-widths decrease when the parameter m increases. For a nonzero constant of integration and for m =2, two couples of trigonometric solutions were obtained and some Jacobi elliptic functions as well. These trigonometric solutions are a pseudo-elliptic bright and a pseudo-elliptic dark solitons. The solutions in each couple are in phase opposition. For m =3, the integral of the first derivative of the square amplitude was established. This integral has elliptic solutions depending on the sign of some parameters. Finally, the effect of higher values of m on the solutions is discussed. It is shown that for higher values of the parameter m , the solution is a sinusoidal function or it tends to infinity. Some amplitudes were plotted for some values of the parameter m . Supplementary Material File (pnlse2025.pdf) Download 3.46 MB Information & Authors Information Version history V1 Version 1 10 December 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords direct integration method jacobi elliptic functions pseudo-elliptic bright soliton pseudo-elliptic dark soliton Authors Affiliations Djouakoua Tcheumanak Franck-Djimitri Universite de Douala View all articles by this author Nicodème Djiedeu 0000-0001-6961-2222 [email protected] Universite de Douala View all articles by this author Wembe Tafo Evariste Universite de Douala View all articles by this author Jean Pierre Nguenang Universite de Douala View all articles by this author Tchawoua Clement Universite de Yaounde 1 Departement de Physique View all articles by this author Metrics & Citations Metrics Article Usage 158 views 194 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Djouakoua Tcheumanak Franck-Djimitri, Nicodème Djiedeu, Wembe Tafo Evariste, et al. Optical solitons of the Nonlinear Schrödinger Equation with a parametric order of non linearity: Exact analytical solutions. Authorea . 10 December 2025. DOI: https://doi.org/10.22541/au.176535020.05719919/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.176535020.05719919/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'a00b3577ef01aa64',t:'MTc3OTYxNDI2Mw=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();