expansion method
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Bornali Phukon ◽  
Akash Anil ◽  
Sanasam Ranbir Singh ◽  
Priyankoo Sarmah

WordNets built for low-resource languages, such as Assamese, often use the expansion methodology. This may result in missing lexical entries and missing synonymy relations. As the Assamese WordNet is also built using the expansion method, using the Hindi WordNet, it also has missing synonymy relations. As WordNets can be visualized as a network of unique words connected by synonymy relations, link prediction in complex network analysis is an effective way of predicting missing relations in a network. Hence, to predict the missing synonyms in the Assamese WordNet, link prediction methods were used in the current work that proved effective. It is also observed that for discovering missing relations in the Assamese WordNet, simple local proximity-based methods might be more effective as compared to global and complex supervised models using network embedding. Further, it is noticed that though a set of retrieved words are not synonyms per se, they are semantically related to the target word and may be categorized as semantic cohorts.

Hengchun Hu ◽  
Xiaodan Li

The nonlocal symmetry of the new (3+1)-dimensional Boussinesq equation is obtained with the truncated Painlev\'{e} method. The nonlocal symmetry can be localized to the Lie point symmetry for the prolonged system by introducing auxiliary dependent variables. The finite symmetry transformation related to the nonlocal symmetry of the integrable (3+1)-dimensional Boussinesq equation is studied. Meanwhile, the new (3+1)-dimensional Boussinesq equation is proved by the consistent tanh expansion method and many interaction solutions among solitons and other types of nonlinear excitations such as cnoidal periodic waves and resonant soliton solution are given.

Liling Shen

In view of the inaccuracy of traditional methods for solving nonlinear equations with variable coefficients in parallel, a new method for solving nonlinear equations with variable coefficients is proposed. Using the generalized symmetry group, the variable coefficient of the equation is taken as a new variable which is the same as the state of the original actual physical field. Some relations between variable coefficient equations and their solutions are found. This paper analyzes the meaning of linear differential equation and nonlinear differential equation, the difference between linear differential equation and nonlinear differential equation and their role in physics, and the necessity of solving nonlinear differential equation. By solving the nonlinear equation with variable coefficients, it can be seen that the general methods to solve the nonlinear equation include scattering inversion, Backlund transform and traveling wave solution. Based on the existing methods for solving nonlinear equations with variable coefficients, the homogeneous balance method is combined with the improved truncated expansion method, truncated expansion method and function reduction method, and the Hopf Cole transform and trial function are combined respectively. The above three methods are used to solve nonlinear equations with variable coefficients. Based on KdV Painleve principle, a parallel method for solving nonlinear equations with variable coefficients is proposed. Finally, it is proved that the method is accurate and effective for the parallel solution of nonlinear equations with variable coefficients.

2022 ◽  
Thilagarajah Mathanaranjan

Abstract In this study, the generalized coupled nonlinear Schrodinger-KdV (NLS-KdV) system is investigated to obtain new optical soliton solutions. This system appears as a model for reciprocity between long and short waves in various of physical settings. Different kind of new soliton solutions including dark, bright, combined dark-bright, singular and combined singular soliton solutions are obtained using two effective methods namely, the extended sinh-Gordon equation expansion method and the solitary wave ansatz method. In addition, the modulation instability analysis of the system is presented based on the standard linearstability analysis. The behaviours of obtained solutions are expressed by 3D graphs.

2022 ◽  
Muslum Ozisik ◽  
Mustafa Bayram ◽  
Aydin Secer ◽  
Melih Cinar

Abstract In this paper, we have successfully extracted novel analytic solutions for the (1+2)-dimensional Chiral non-linear Schrödinger (NLS) equation by modified extended tanh expansion method combined with new Riccati solutions (METEM-cNRCS) as far as we know. When a wave transformation is applied to the considered Chiral NLS equation, a nonlinear ODE is obtained. Assuming the solutions of ODE have a form as the method suggests, and substituting the trial solutions to the ODE, we get a polynomial. Gathering the coefficients with the same power in the polynomial, we acquire an algebraic equation system. So, we may obtain the abundant solutions of the (1+2)-dimensional Chiral NLS equation by solving the system via Maple. The plots of some solutions are demonstrated to explain the dynamics of the solutions. It is expected that the results of the paper are a guide for future works in traveling wave theory.

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