Characterizing the physical and dynamical properties of lump, rogue waves and their interactions for a cascaded system with spatio-temporal dispersion and Kerr nonlinearity

Sarfaraz Ahmed; Atef F. Hashem; Syed T. R. Rizvi; Aly R. Seadawy; Sarfaraz Ahmed; Atef F. Hashem; Syed T. R. Rizvi; Aly R. Seadawy

doi:10.3934/math.2025739

AIMS Mathematics

2025, Volume 10, Issue 7: 16498-16525. doi: 10.3934/math.2025739

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Research article

Characterizing the physical and dynamical properties of lump, rogue waves and their interactions for a cascaded system with spatio-temporal dispersion and Kerr nonlinearity

1.
College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
4.
Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, 41411, Saudi Arabia

Received: 22 May 2025 Revised: 02 July 2025 Accepted: 09 July 2025 Published: 22 July 2025
MSC : 35B10, 35C07, 35C08, 35Q35

This article uses Hirota's bilinear method (HBM) and appropriate transformations to investigate several lump solution forms in a cascaded system with spatiotemporal dispersion (STD) and Kerr law nonlinearity (KLN). The vector-coupled nonlinear Schrödinger equation is the mathematical model that describes how different solitons propagate through a cascaded system. Using the positive quadratic assumption in bilinear form, we evaluate lump solutions. By using the single and double exponential ansatz in bilinear form, respectively, we additionally investigate lump single-strip and double-strip soliton interactions. Furthermore, by using trigonometric and hyperbolic functions, respectively, we are able to find lump periodic and rogue wave solutions. Additionally, we discuss and illustrate the geometry of our solutions in multiple dimensions, such as contour plots and 3D. We also compute the stability of our solutions.
- the cascaded system,
- lump solitons,
- rogue wave solution,
- ansatz transformations,
- Hirota's bilinear method
Citation: Sarfaraz Ahmed, Atef F. Hashem, Syed T. R. Rizvi, Aly R. Seadawy. Characterizing the physical and dynamical properties of lump, rogue waves and their interactions for a cascaded system with spatio-temporal dispersion and Kerr nonlinearity[J]. AIMS Mathematics, 2025, 10(7): 16498-16525. doi: 10.3934/math.2025739

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Abstract

This article uses Hirota's bilinear method (HBM) and appropriate transformations to investigate several lump solution forms in a cascaded system with spatiotemporal dispersion (STD) and Kerr law nonlinearity (KLN). The vector-coupled nonlinear Schrödinger equation is the mathematical model that describes how different solitons propagate through a cascaded system. Using the positive quadratic assumption in bilinear form, we evaluate lump solutions. By using the single and double exponential ansatz in bilinear form, respectively, we additionally investigate lump single-strip and double-strip soliton interactions. Furthermore, by using trigonometric and hyperbolic functions, respectively, we are able to find lump periodic and rogue wave solutions. Additionally, we discuss and illustrate the geometry of our solutions in multiple dimensions, such as contour plots and 3D. We also compute the stability of our solutions.

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