Distributed representations enable robust multi-timescale symbolic computation in neuromorphic hardware by Madison Cotteret, Hugh Greatorex, Alpha Renner, Junren Chen, Emre Neftci, Huaqiang Wu, Giacomo Indiveri, Martin Ziegler, Elisabetta Chicca

“…This work introduces a scalable approach to embed robust symbolic computation through recurrent dynamics into neuromorphic hardware, without requiring parameter fine-tuning or significant platform-specific optimisation. …”
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Exact Solutions to a Generalized Bogoyavlensky-Konopelchenko Equation via Maple Symbolic Computations by Shou-Ting Chen, Wen-Xiu Ma

“…The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are made for solving both the nonlinear equation and the corresponding bilinear equation. …”
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Computation of symmetries of rational surfaces by Juan Gerardo Alcázar, Carlos Hermoso, Hüsnü Anıl Çoban, Uğur Gözütok

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Lump-type kink wave phenomena of the space-time fractional phi-four equation by Khudhayr A. Rashedi, Musawa Yahya Almusawa, Hassan Almusawa, Tariq S. Alshammari, Adel Almarashi

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New solutions to a category of nonlinear PDEs by Bacui Li, Fuzhang Wang

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Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces by Minghao Guo, Tieru Wu, Shugong Zhang

“…We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. …”
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GroupFound: An effective approach to detect suspicious accounts in online social networks by Bo Feng, Qiang Li, Xiaowen Pan, Jiahao Zhang, Dong Guo

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A Novel Histogram Region Merging Based Multithreshold Segmentation Algorithm for MR Brain Images by Siyan Liu, Xuanjing Shen, Yuncong Feng, Haipeng Chen

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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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New Interaction Solutions for a (2 + 1)-Dimensional Vakhnenko Equation by Qing Meng, Bin He

“…By using Hirota’s transformation combined with the three-wave method and with symbolic computation, some interaction solutions which include interaction solutions between exponential and trigonometric functions and interaction solutions between exponential and trigonometric and hyperbolic functions are presented.…”
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Analysis of the Symmetries and Conservation Laws of the Nonlinear Jaulent-Miodek Equation by Mehdi Nadjafikhah, Mostafa Hesamiarshad

“…And conservation laws of the J-M equation are presented with two steps: firstly, finding multipliers for computation of conservation laws and, secondly, symbolic computation of conservation laws will be applied.…”
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Exact Solutions for the Wick-Type Stochastic Schamel-Korteweg-de Vries Equation by Xueqin Wang, Yadong Shang, Huahui Di

“…With the aid of symbolic computation and Hermite transformation, by employing the (G′/G,1/G)-expansion method, we derive the new exact travelling wave solutions, which include hyperbolic and trigonometric solutions for the considered equations.…”
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Lump and Lump-Type Solutions of the Generalized (3+1)-Dimensional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equation by Yanni Zhang, Jing Pang

“…Based on the Hirota bilinear form of the generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation, the lump and lump-type solutions are generated through symbolic computation, whose analyticity can be easily achieved by taking special choices of the involved parameters. …”
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New Nonlinear Systems Admitting Virasoro-Type Symmetry Algebra and Group-Invariant Solutions by Lizhen Wang, Qing Huang, Yanmei Di

“…With the aid of symbolic computation by Maple, we extend the application of Virasoro-type symmetry prolongation method to coupled systems with two-component nonlinear equations. …”
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The Improved Riccati Equation Method and Exact Solutions to mZK Equation by Xiaofeng Li

“…The method appears to be easier and more convenient by means of a symbolic computation system. Of course, it is also effective to solve other nonlinear evolution equations in mathematical physics.…”
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The Study of the Solution to a Generalized KdV-mKdV Equation by Xiumei Lv, Tengwei Shao, Jiacheng Chen

“…A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is employed to investigate a generalized KdV-mKdV equation which possesses high-order nonlinear terms. …”
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Rational Solutions for the (2+1)-Dimensional Modified KdV-CBS Equation by Yan Li, Temuer Chaolu, Yuexing Bai

“…In this paper, with the help of symbolic computation, three types of rational solutions for the (2+1)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation are derived. …”
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Abundant Interaction Solutions of Sine-Gordon Equation by DaZhao Lü, YanYing Cui, ChangHe Liu, ShangWen Wu

“…With the help of computer symbolic computation software (e.g., Maple), abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. …”
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Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs by Na Lv, Xuegang Yuan, Jinzhi Wang

“…With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation by Lou’s direct method which is based on Lax pairs. …”
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Physics Informed by Deep Learning: Numerical Solutions of Modified Korteweg-de Vries Equation by Yuexing Bai, Temuer Chaolu, Sudao Bilige

“…In this paper, with the aid of symbolic computation system Python and based on the deep neural network (DNN), automatic differentiation (AD), and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization algorithms, we discussed the modified Korteweg-de Vries (mkdv) equation to obtain numerical solutions. …”
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