Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework by Yuan Kong, Xing-Chen Liu, Huan-He Dong, Ming-Shuo Liu, Chun-Ming Wei, Xiao-Qian Huang, Yong Fang

“…Hirota’s direct method is one significant way to obtain solutions of soliton equations, but it is rarely studied under the time scale framework. …”
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Solitons of the Twin-Core Couplers with Fractional Beta Derivative Evolution in Optical Metamaterials via Two Distinct Methods by Meryem Odabasi Koprulu, Zehra Pinar Izgi

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Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior by Muhammad Aziz ur Rehman, Muhammad Bilal Riaz, Muhammad Iqbal

“…To solve the Jimbo–Miwa equation, a modified Khater method has been employed to generate various forms of soliton wave structures. Exact solutions to this equation are considered important for the complete understanding of the dynamics of waves in a physical model. …”
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Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics by Sheng Zhang, Sen Zhao, Bo Xu

“…It is shown that the time-varying coefficient functions affect the spatiotemporal structures and the propagation velocities of the obtained semidiscrete one-soliton solutions, two-soliton solutions, and three-soliton solutions.…”
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New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques by Umair Asghar, Muhammad Imran Asjad, Yasser Salah Hamed, Ali Akgul, Murad Khan Hassani

“…These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. …”
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Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches by Ibrahim Alraddadi, Faisal Alsharif, Sandeep Malik, Hijaz Ahmad, Taha Radwan, Karim K. Ahmed

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Three-dimensional matter wave soliton transformation between different optical lattices in a cold Rydberg atomic system by Wei Peng, Yu Wang, Yuan Zhao, Zhuo Fan, Siliu Xu

“…Abstract We present a novel approach to realize three-dimensional (3D) matter wave solitons (MWSs) transformation between different optical potential wells by manipulating their depths and centers. …”
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The Interactions of N-Soliton Solutions for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation by Xiangrong Wang, Xiaoen Zhang, Yong Zhang, Huanhe Dong

“…Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient eAij; when eAij=0, the soliton fusion and fission will happen; when eAij≠0, the pursuing collision will occur. …”
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Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques by Imran Siddique, Khush Bukht Mehdi, M. Ali Akbar, Hamiden Abd El-Wahed Khalifa, Asim Zafar

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Computer two dimensional maps of loop soliton lattice systems using the new approach to the no integrability Aesthetic field equations by M. Muraskin

“…We show that there are varieties of somewhat different loop soliton lattices when we specify an integration path in No Integrability Aesthetic Field Theory. …”
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A novel approach to construct optical solitons solutions of complex Ginzburg–Landau equation with five distinct forms of nonlinearities by F. Gassem, Osman Osman, Faez Alqarni, Khaled Aldwoah, Fathea M. Osman Birkea, Manel Hleili

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Collisional Solitons Described by Two-Sided Beta Time Fractional Korteweg-de Vries Equations in Fluid-Filled Elastic Tubes by Sharmin Akter, M. D. Hossain, M. F. Uddin, M. G. Hafez

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Algebro-Geometric Solutions of a (2+1)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy by Xiaohong Chen

“…The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy. …”
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A Soliton Hierarchy Associated with a Spectral Problem of 2nd Degree in a Spectral Parameter and Its Bi-Hamiltonian Structure by Yuqin Yao, Shoufeng Shen, Wen-Xiu Ma

“…Associated with so~(3,R), a new matrix spectral problem of 2nd degree in a spectral parameter is proposed and its corresponding soliton hierarchy is generated within the zero curvature formulation. …”
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Abundant Exact Soliton Solutions of the (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation Based on the Jacobi Elliptic Function Ideas by Qinghao Zhu, Jianming Qi

“…Therefore, further studying EMVJEEM may help researchers to seek for more soliton solutions to other nonlinear differential equations.…”
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Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method by Wafaa B. Rabie, Hamdy M. Ahmed, Taher A. Nofal, E. M. Mohamed

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Breather, lump and other wave profiles for the nonlinear Rosenau equation arising in physical systems by Baboucarr Ceesay, Muhammad Zafarullah Baber, Nauman Ahmed, Muhammad Waqas Yasin, Wael W. Mohammed

Subjects: “…Soliton…”
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Compactones, soluciones de ecuaciones no lineales con estructura tipo esferas duras by Máximo Agüero Granados, Jorge Bernal, Guadalupe Frias, Mauricio Paulin

Subjects: “…solitones…”
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Dinámica de la molécula más importante de la vida: el ADN. I. Modelos lineales y no lineales by Lorena Ramírez Reyes, Ricardo García Salcedo, Máximo Agüero Granados, Edgar Villagrán Vargas

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Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation by Shuxin Yang, Zhao Zhang, Biao Li

“…Soliton molecules of the (2 + 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived by N-soliton solutions and a new velocity resonance condition. …”
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