Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems by Vladimir Varlamov

“…Riesz potentials (also called Riesz fractional derivatives) and their Hilbert transforms are computed for the Korteweg-de Vries soliton. They are expressed in terms of the full-range Hurwitz Zeta functions 𝜁+(𝑠,𝑎) and 𝜁−(𝑠,𝑎). …”
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Existence and Uniqueness of Positive Solitons for a Second-Order Difference Equation by Xinfu Li, Guang Zhang, Ying Wang

“…By using sub- and upper-solution method, the existence of bounded positive solutions and the existence and uniqueness of positive solitons will be established. To this end, the Dirichlet eigenvalue problem with positive and negative coefficients is considered, and a general sub- and upper-solution theorem is also obtained.…”
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(In)stability of symbiotic vortex-bright soliton in holographic immiscible binary superfluids by Yu-Ping An, Li Li

“…Abstract Symbiotic vortex-bright soliton structures with non-trivial topological charge in one component are found to be robust in immiscibel two-component superfluids, due to the effective potential created by a stable vortex in the other component. …”
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Solitonic Solutions for Homogeneous KdV Systems by Homotopy Analysis Method by Mohammed Ali, Marwan Alquran, Mahmoud Mohammad

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Soliton-like excitation in a nonlinear model of DNA dynamics with viscosity by Conrad Bertrand Tabi, Alidou Mohamadou, Timoleon Crepin Kofane

Subjects: “…bubble soliton…”
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Non-autonomous Ginzburg-Landau solitons using the He-Li mapping method by Maximino Pérez Maldonado, Haret C. Rosu, Elizabeth Flores Garduño

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Schur-type inequality for solitonic hypersurfaces in $ (k, \mu) $-contact metric manifolds by Mohd Danish Siddiqi, Fatemah Mofarreh

Subjects: “…gradient $ r $-almost newton-ricci-yamabe solitons…”
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Cusped and Smooth Solitons for the Generalized Camassa-Holm Equation on the Nonzero Constant Pedestal by Dong Li, Yongan Xie, Shengqiang Tang

“…Our procedure shows that the generalized Camassa-Holm equation with nonzero constant boundary has cusped and smooth soliton solutions. Mathematical analysis and numerical simulations are provided for these traveling soliton solutions of the generalized Camassa-Holm equation. …”
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Bi-Integrable Couplings of a New Soliton Hierarchy Associated with SO(4) by Yan Cao, Liangyun Chen, Baiying He

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Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation by Bo Ren

“…The multisoliton solutions of the higher-order Boussinesq equation are obtained by introducing dependent variable transformation. The soliton molecule and asymmetric soliton of the higher-order Boussinesq equation can be constructed by the velocity resonance mechanism. …”
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The Modified Coupled Hirota Equation: Riemann-Hilbert Approach and N-Soliton Solutions by Siqi Xu

“…The Cauchy initial value problem of the modified coupled Hirota equation is studied in the framework of Riemann-Hilbert approach. The N-soliton solutions are given in a compact form as a ratio of (N+1)×(N+1) determinant and N×N determinant, and the dynamical behaviors of the single-soliton solution are displayed graphically.…”
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Solitones singulares y regulares en la ecuación no lineal de Kadomtsev-Petvishvili by Erick Flores Romero, Máximo Agüero Granados

Subjects: “…solitones…”
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Symmetry Breaking Soliton, Breather, and Lump Solutions of a Nonlocal Kadomtsev–Petviashvili System by Hong-Yu Wu, Jin-Xi Fei, Zheng-Yi Ma, Jun-Chao Chen, Wen-Xiu Ma

“…By introducing an extended Bäcklund transformation, symmetry breaking soliton, symmetry breaking breather, and symmetry breaking lump solutions for this system are presented through the established Hirota bilinear form. …”
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Manipulation of 2D and 3D Magnetic Solitons Under the Influence of DMI Gradients by Rayan Moukhader, Davi Rodrigues, Eleonora Raimondo, Vito Puliafito, Bruno Azzerboni, Mario Carpentieri, Abbass Hamadeh, Giovanni Finocchio, Riccardo Tomasello

“…Magnetic solitons hold great promise for token-based computing applications due to their intrinsic properties, including small size, topological stability, ultra-low power manipulation, and potentially ultra-fast operation. …”
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Soliton Molecules and Full Symmetry Groups to the KdV-Sawada-Kotera-Ramani Equation by Na Xiong, Ya-Xuan Yu, Biao Li

“…By N-soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate the resonances of solitons in one-dimensional space. …”
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Fractional Soliton and Semirational Solutions of a Fractional Two-Component Generalized Hirota Equation by Sheng Zhang, Feng Zhu, Bo Xu

“…The main purpose of this article is to extend the DT and GDT to a conformable fractional two-component generalized Hirota (TCGH) equation for revealing novel dynamic characteristics of fractional soliton and semirational solutions. As for the main contributions, specifically, we propose a fractional form of the TCGH equation, provide the associated fractional Lax pair, and obtain fractional soliton and semirational solutions of the fractional TCGH equation by constructing its fractional DT and GDT. …”
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All-optical azimuthal trapping of dissipative Kerr multi-solitons for relative noise suppression by Pradyoth Shandilya, Shao-Chien Ou, Jordan Stone, Curtis Menyuk, Miro Erkintalo, Kartik Srinivasan, Grégory Moille

“…Temporal cavity solitons, or dissipative Kerr solitons (DKSs) in integrated microresonators, are essential for deployable metrology technologies. …”
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Single soliton microcomb combined with optical phased array for parallel FMCW LiDAR by Jingye Chen, Wenlei Li, Zhe Kang, Zongxing Lin, Shi Zhao, Daixin Lian, Jijun He, Dongmei Huang, Daoxin Dai, Yaocheng Shi

“…The modulation bandwidth of parallel modulation of the microcomb is beyond the modulation region of single soliton microcomb. The result paves the way for developing all-solid-state and ultrahigh-frame-rate coherent LiDAR systems.…”
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Lump and Mixed Rogue-Soliton Solutions of the (2 + 1)-Dimensional Mel’nikov System by Yue-jun Deng, Rui-yu Jia, Ji Lin

“…By combining a rational function and different exponential functions, mixed solutions between the lump and soliton are derived. These solutions describe the interaction phenomena of the lump-bright soliton with fission and fusion, the half-line rogue wave with a bright soliton, and a rogue wave excited from the bright soliton pair, respectively. …”
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Residual Symmetry, Bäcklund Transformation, and Soliton Solutions of the Higher-Order Broer-Kaup System by Yarong Xia, Ruoxia Yao, Xiangpeng Xin

“…In order to find more general solution of HBK system, we further generalize the residual symmetry method to the consistent tanh expansion (CTE) method and prove that the HBK system is CTE solvable, then the resonant soliton solutions and interaction solutions among different nonlinear excitations are obtained by the CET method.…”
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