Broer-Kaup System with Corrections via Inverse Scattering Transform by Xueru Wang, Junyi Zhu

“…Based on the inverse scattering transform, we extend the perturbation theory to discuss the adiabatic approximate solution and ε-order approximate solution of one soliton to the Broer-Kaup system with corrections.…”
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The Hamiltonian Structure and Algebrogeometric Solution of a 1 + 1-Dimensional Coupled Equations by Hongfei Pan, Tiecheng Xia

“…A 1 + 1-dimensional coupled soliton equations are decomposed into two systems of ordinary differential equations. …”
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Some Analytical Solitary Wave Solutions for the Generalized q-Deformed Sinh-Gordon Equation: ∂2θ/∂z∂ξ=αsinhq⁡(βθγ)p-δ by H. Eleuch

“…We introduce the generalized q-deformed Sinh-Gordon equation and derive analytical soliton solutions for some sets of parameters. This new defined equation could be useful for modeling physical systems with violated symmetries.…”
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Exact Solution of (4+1)-Dimensional Boiti–Leon–Manna–Pempinelli Equation by Qili Hao

“…Based on the Hirota bilinear method, using the heuristic function method and mathematical symbolic computation system, various exact solutions of the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation including the block kink wave solution, block soliton solution, periodic block solution, and new composite solution are obtained. …”
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Expanded (G/G2) Expansion Method to Solve Separated Variables for the 2+1-Dimensional NNV Equation by Yong Meng

“…By using this method, the solution to the detached variables of the symmetric extended form of the 2+1-dimensional NNV equation can be solved, also the soliton structure and fractal structure of Dromion can be studied well.…”
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A New Auto-Bäcklund Transformation of the KdV Equation with General Variable Coefficients and Its Application by Chunping Liu

“…Then, based on the new auto-BT in which there is only one quadratic homogeneity equation to be solved, an exact soliton-like solution containing 2-solitary wave is given.…”
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Bäcklund Transformation and Exact Solutions to a Generalized (3 + 1)-Dimensional Nonlinear Evolution Equation by Yali Shen, Ying Yang

“…Based on the Hirota bilinear method, the N-soliton solution and bilinear Bäcklund transformation (BBT) with explicit formulas are successfully constructed. …”
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Description of Dispersive Wave Emission and Supercontinuum Generation in Silicon Waveguides Using Split-Step Fourier and Runge-Kutta Integration Methods by Xuefeng Li

“…Based on solving numerically the generalized nonlinear Schrödinger equation describing the propagation of high order femtosecond soliton in silicon waveguide under certain parametric conditions by the split-step Fourier and Runge-Kutta integration methods, dispersive wave emission and supercontinuum generation in silicon waveguides are numerically investigated by propagating femtosecond solitons. …”
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Binormal Motion of Curves with Constant Torsion in 3-Spaces by Josu Arroyo, Óscar J. Garay, Álvaro Pámpano

“…Using the Gauss-Codazzi equations, we obtain filaments evolving with constant torsion which arise from extremal curves of curvature energy functionals. They are “soliton” solutions in the sense that they evolve without changing shape.…”
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The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source by Yali Shen, Fengqin Zhang, Xiaomei Feng

“…In order to further prove its integrality, we give its bilinear form and construct its bilinear Bäcklund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form.…”
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The Study of the Solution to a Generalized KdV-mKdV Equation by Xiumei Lv, Tengwei Shao, Jiacheng Chen

“…Some new solutions including the Jacobi elliptic function solutions, the degenerated soliton-like solutions, and the triangle function solutions to the equation are obtained.…”
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Finite volume expectation values in the sine-Gordon model by Árpád Hegedűs

“…We tested our formulas in the pure multi-soliton sector of the theory. In the ultraviolet limit, we checked our results against Liouville 3-point functions, while in the infrared limit, we evaluated our formulas in the semi-classical limit and compared them up to 2-particle contributions against the semi-classical limit of the previously conjectured LeClair-Mussardo type formula. …”
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Phase Transitions of the BTZ Black Hole in New Massive Gravity by Yun Soo Myung

“…For m2l2>1/2 with m2 being the mass parameter of fourth-order terms and l2 AdS3 curvature radius, the Hawking-Page phase transition occurs between the BTZ black hole and AdS (thermal) soliton. For m2l2<1/2, however, this transition unlikely occurs but a phase transition between the BTZ black hole and the massless BTZ black hole is possible to occur. …”
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Double Periodic Wave Solutions of the (2 + 1)-Dimensional Sawada-Kotera Equation by Zhonglong Zhao, Yufeng Zhang, Tiecheng Xia

“…The relations between the periodic wave solutions and soliton solutions are rigorously established by a limiting procedure.…”
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Graviatoms with de Sitter Interior by Irina Dymnikova, Michael Fil’chenkov

“…It is a gravitationally bound quantum system consisting of a nucleus represented by a regular primordial black hole (RPBH), its remnant or gravitational vacuum soliton G-lump, and a charged particle. We estimate probability of formation of RPBHs and G-lumps in the early Universe and evaluate energy spectrum and electromagnetic radiation of graviatom which can in principle bear information about a fundamental symmetry scale responsible for de Sitter interior and serve as its observational signatures.…”
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Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions by Weiguo Rui

“…Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. …”
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Bell Polynomials Approach Applied to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation by Wen-guang Cheng, Biao Li, Yong Chen

“…The integrable constraint conditions on variable coefficients can be naturally obtained in the procedure of applying the Bell polynomials approach. Moreover, the N-soliton solutions of the equation are constructed with the help of the Hirota bilinear method. …”
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An Efficient Approach to Numerical Study of the MRLW Equation with B-Spline Collocation Method by Seydi Battal Gazi Karakoç, Turgut Ak, Halil Zeybek

“…Three test problems including the single soliton and interaction of two and three solitons are studied to validate the proposed method by calculating the error norms L2 and L∞ and the invariants I1, I2, and I3. …”
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Lax Triples for Integrable Surfaces in Three-Dimensional Space by Jan L. Cieśliński, Artur Kobus

“…Finally, the obtained results are interpreted in the context of the soliton surfaces approach.…”
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Different Wave Structures for the (2+1)-Dimensional Korteweg-de Vries Equation by Chun-Rong Qin, Jian-Guo Liu, Wen-Hui Zhu, Guo-Ping Ai, M. Hafiz Uddin

“…Based on the extended homoclinic test technique, some new double periodic-soliton solutions are presented. Finally, some 3D and density plots are simulated and displayed to respond the dynamic behavior of these obtained solutions.…”
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