Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation by Huanhe Dong, Yanfeng Zhang, Yongfeng Zhang, Baoshu Yin

“…As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.…”
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Dynamic Behaviors and Analytical Solutions of the Damped (2+1)-Dimensional Nonlinear Schrödinger Equation by Yongyi Gu, Feng Ye, Baixin Chen, Najva Aminakbari

“…By considering various values of parameters, dynamic behaviors of bright, dark soliton, period wave, and kink solitary solutions are displayed with different amplitudes and directions in 3D graphs, lines, contour maps, and time evolution plots. …”
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Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System by Weiguo Rui, Yao Long

“…Many traveling wave solutions of nonsingular type and singular type, such as solitary wave solutions, kink wave solutions, loop soliton solutions, compacton solutions, smooth periodic wave solutions, periodic kink wave solution, singular wave solution, and singular periodic wave solution are obtained. …”
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Study of Dust-Acoustic Multisoliton Interactions in Strongly Coupled Dusty Plasmas by Najah Kabalan, Mahmoud Ahmad, Ali Asad

“…The effect of the structure parameter on the compressibility of dust grains and soliton behavior in a dusty plasma system consisting of Maxwellian electrons, ions, and dust grains charged with a negative charge has been studied. …”
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A Numerical Solution for Hirota-Satsuma Coupled KdV Equation by M. S. Ismail, H. A. Ashi

“…The interaction of two solitons, three solitons, and birth of solitons is also discussed.…”
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Abundant Symmetry-Breaking Solutions of the Nonlocal Alice–Bob Benjamin–Ono System by Wang Shen, Zheng-Yi Ma, Jin-Xi Fei, Quan-Yong Zhu, Jun-Chao Chen

“…By introducing an extended Bäcklund transformation, the symmetry-breaking soliton, breather, and lump solutions for this system are obtained through the derived Hirota bilinear form. …”
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The Extended Trial Equation Method for Some Time Fractional Differential Equations by Yusuf Pandir, Yusuf Gurefe, Emine Misirli

“…As a result, some new exact solutions to these nonlinear problems are successfully constructed such as elliptic integral function solutions, Jacobi elliptic function solutions, and soliton solutions.…”
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F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation by Ali Filiz, Mehmet Ekici, Abdullah Sonmezoglu

“…When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. …”
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A New Class of Contact Pseudo Framed Manifolds with Applications by K. L. Duggal

“…We also have established a link of CPF-hypersurfaces with curvature, affine, conformal collineations symmetries, and almost Ricci soliton manifolds, supported by three applications. …”
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Numerical collocation technique for solving modified equal width wave equation by Aqib Zafar, Shyam Sundra Santra, Muhammad Nasir

“…The proposed scheme of major equation is tested by three ways: Single Soliton Wave, train of Solitary Waves and final birth solution. …”
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Numerical Modeling of the Internal Dispersive Shock Wave in the Ocean by Tatiana Talipova, Efim Pelinovsky, Oxana Kurkina, Andrey Kurkin

“…It is shown that a sharp drop (like kink in the soliton theory) in the depth of the thermocline is conserved at a distance of one–three kilometers, and then it is transformed into dispersive shock waves (shock wave with undulations).…”
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Propagation of Nonlinear Dust-Acoustic Waves in a Self-Gravitating Collision Magnetized Dusty Plasma in Earth’s Magnetosphere by Aljawhara H. Almuqrin, Mohammed F. Alotiby, R. E. Tolba

“…It has been found that there can be a relationship between the appearance of soliton waves and electromagnetic waves, as well as between shock-like waves and periodic travelling waves. …”
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(2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves by Chunlei Wang, Yong Zhang, Baoshu Yin, Xiaoen Zhang

“…With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given.…”
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Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method by Mojtaba Nazari, Faisal Salah, Zainal Abdul Aziz, Merbakhsh Nilashi

“…The resulted HAM solution at 8th-order and 14th-order approximation is then compared with that of the exact soliton solutions of KdV and Burgers equations, respectively, and shown to be in excellent agreement.…”
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The New Solitary Solutions to the Time-Fractional Coupled Jaulent–Miodek Equation by Guiping Shen, Jalil Manafian, Syed Maqsood Zia, Dinh Tran Ngoc Huy, Trung-Hieu Le

“…Materials such as photovoltaic-photorefractive, polymer, and organic contain spatial solitons and optical nonlinearities, which can be identified by seeking from energy-dependent Schrödinger potential. …”
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An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions by A. H. Bhrawy, M. A. Alghamdi, Eman S. Alaidarous

“…In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.…”
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Nonautonomous Motion Study on Accelerated and Decelerated Lump Waves for a (3 + 1)-Dimensional Generalized Shallow Water Wave Equation with Variable Coefficients by Wei-Qin Chen, Qing-Feng Guan, Chao-Fan Jiang, Fei-Fan Zhang, Lei Wang

“…The periodic fission and fusion interaction between a lump wave and a kink soliton is discussed graphically.…”
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Analytical Solutions of the Fractional Complex Ginzburg-Landau Model Using Generalized Exponential Rational Function Method with Two Different Nonlinearities by Ghazala Akram, Maasoomah Sadaf, M. Atta Ullah Khan, Hasan Hosseinzadeh

“…A variety of exact traveling wave solutions are reported including dark, bright, and kink soliton solutions. The nature of the optical solitons is demonstrated through the graphical representations of the acquired solutions for variation in the fractional order of derivative. …”
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Approximate Analytical Solution for the Forced Korteweg-de Vries Equation by Vincent Daniel David, Mojtaba Nazari, Vahid Barati, Faisal Salah, Zainal Abdul Aziz

“…Finally, this form of HAM solution is compared with the analytical soliton-type solution of fKdV equation as derived by Zhao and Guo. …”
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Transient bifurcation induced rocket acceleration leading to a relativistic bulk medium induced by designed high-intensity lasers by Ryutaro Matsui, Yasuaki Kishimoto

“…The other is the fast process of the transient bifurcation of the shock to a soliton leading to an explosion, which splits the structure into two shock structures propagating in opposite directions, i.e., one is boosted forward as the reaction of the other ejected backward as a fuel. …”
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