We have introduced various novel soliton waves and other analytic wave solutions for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities. The modified extended direct algebraic method governs the transmission of various solitons with different effects. The combination of this system enables the obtaining of analytical soliton solutions with some unique behaviors, including bright, dark, and mixed dark-bright soliton solutions; singular soliton solutions; singular periodic, exponential, rational wave solutions; and Jacobi elliptic function solutions. These results realize the stability of the nonlinear waves' propagation in a high-nonlinear-dispersion medium that is illustrated using 2D and 3D visuals and contour graphical diagrams of the output solutions. This research focused on determining exact soliton solutions under certain parameter conditions and evaluating the stability and reliability of the soliton solutions based on the used modified extended direct algebraic method. This will be useful for many various domains in technology and physics, such as biology, optics, and plasma physical science. At the end, we use modulation instability analysis to assess the stability of the wave solutions obtained.
Citation: Abeer S. Khalifa, Hamdy M. Ahmed, Niveen M. Badra, Wafaa B. Rabie, Farah M. Al-Askar, Wael W. Mohammed. New soliton wave structure and modulation instability analysis for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities[J]. AIMS Mathematics, 2024, 9(9): 26166-26181. doi: 10.3934/math.20241278
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We have introduced various novel soliton waves and other analytic wave solutions for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities. The modified extended direct algebraic method governs the transmission of various solitons with different effects. The combination of this system enables the obtaining of analytical soliton solutions with some unique behaviors, including bright, dark, and mixed dark-bright soliton solutions; singular soliton solutions; singular periodic, exponential, rational wave solutions; and Jacobi elliptic function solutions. These results realize the stability of the nonlinear waves' propagation in a high-nonlinear-dispersion medium that is illustrated using 2D and 3D visuals and contour graphical diagrams of the output solutions. This research focused on determining exact soliton solutions under certain parameter conditions and evaluating the stability and reliability of the soliton solutions based on the used modified extended direct algebraic method. This will be useful for many various domains in technology and physics, such as biology, optics, and plasma physical science. At the end, we use modulation instability analysis to assess the stability of the wave solutions obtained.
Since its initiation in 1979, the Canadian Applied and Industrial Mathematics Society — Société Canadienne de Mathématiques Appliquées et Industrielles (CAIMS–SCMAI) has gained a growing presence in industrial, mathematical, scientific, and technological circles within and outside of Canada. Its members contribute to state-of-the-art research in industry, natural sciences, medicine and health, finance, physics, engineering, and more. The annual meetings are a highlight of the year. CAIMS–SCMAI is an active member society of the International Council for Industrial and Applied Mathematics, which hosts the prestigious ICIAM Congresses every four years.
Canadian Applied and Industrial Mathematics is at the forefront of scientific and technological development. We use advanced mathematics to tackle real-world problems in science and industry and develop new theories to analyse structures that arise from the modelling of real-world problems.
Applied Mathematics has evolved from traditional applications in areas such as fluids, mechanics, and physics, to modern topics such as medicine, health, biology, data science, finance, nano-tech, etc. Its growing importance in all aspects of life, health, and management increases the need for publication venues for high-level applied and industrial mathematics. Hence CAIMS–SCMAI decided to start a scientific journal called Mathematics in Science and Industry (MSI) to add value to the discussion of applied and industrial mathematics worldwide.
Submissions to MSI in all areas of applied and industrial mathematics are welcome (https://caims.ca/mathematics_in_science_and_industry/). We offer a timely and high-quality review process, and papers are published online as open access, with the publication fee being covered by CAIMS for the first five years.
MSI is honored that leading experts in industrial and applied mathematics have offered their support as editors:
Editors in Chief:
● Thomas Hillen (University of Alberta, thillen@ualberta.ca)
● Ray Spiteri (University of Saskatchewan, spiteri@cs.usask.ca)
Associate Editors:
● Lia Bronsard (McMaster University)
● Richard Craster (Imperial College of London, UK)
● David Earn (McMaster University)
● Ronald Haynes (Memorial University)
● Jane Heffernan (York University)
● Nicholas Kevlahan (McMaster University)
● Yong-Jung Kim (KAIST, Korea)
● Mark Lewis (University of Alberta)
● Kevin J. Painter (Heriot-Watt University, UK)
● Vakhtang Putkaradze (ATCO)
● Katrin Rohlf (Ryerson University)
● John Stockie (Simon Fraser University)
● Jie Sun (Huawei, Hong Kong)
● Justin Wan (University of Waterloo)
● Michael Ward (University of British Columbia)
● Tony Ware (University of Calgary)
● Brian Wetton (University of British Columbia)
The first eight papers of MSI, presented here, are published as special issue in AIMS Mathematics. They showcase a broad representation of applied mathematics that touches the interests of Canadian researchers and our many collaborators around the world. The science that we present here is not exclusively "Canadian", but we hope that through the new journal MSI, we can contribute to scientific dissemination of knowledge and add Canadian values to the scientific discussion.
The next issue of MSI is planned for the fall of 2020 and is expected to appear again as a special issue of AIMS Mathematics.
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Figures(5)
Abeer S. Khalifa, Hamdy M. Ahmed, Niveen M. Badra, Wafaa B. Rabie, Farah M. Al-Askar, Wael W. Mohammed. New soliton wave structure and modulation instability analysis for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities[J]. AIMS Mathematics, 2024, 9(9): 26166-26181. doi: 10.3934/math.20241278
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