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1. Abundant mixed lump-soliton solutions to the BKP equation

   https://doi.org/DOI:10.4208/eajam.210917.051217a  

   Yang, Jin-Yun ; Ma, Wen-Xiu ; Qin, Zhenyun ( June 2018 , Analysis and mathematical physics)

   Based on the Hirota bilinear form of the (2 + 1)-dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperboliccosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions. 

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2. Lump solutions to a generalized Bogoyavlensky-Konopelchenko equation

   Chen, Shou-Ting ; Ma, Wen-Xiu ( June 2018 , Frontiers of Mathematics in China)

   A (2 + 1)-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered. Starting with its Hirota bilinear form, a class of explicit lump solutions is computed through conducting symbolic computations with Maple, and a few plots of a specicpresented lump solution are made to shed light on the characteristics of lumps. The result provides a new example of (2 + 1)-dimensional nonlinear partial differential equations which possess lump solutions. 

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3. Lump chains in the KP‐I equation

   https://doi.org/10.1111/sapm.12420  

   Lester, Charles ; Gelash, Andrey ; Zakharov, Dmitry ; Zakharov, Vladimir ( July 2021 , Studies in Applied Mathematics)

   We construct a broad class of solutions of the Kadomtsev–Petviashvili (KP)‐I equation by using a reduced version of the Grammian form of the‐function. The basic solution is a linear periodic chain of lumps propagating with distinct group and wave velocities. More generally, our solutions are evolving linear arrangements of lump chains, and can be viewed as the KP‐I analogues of the family of line‐soliton solutions of KP‐II. However, the linear arrangements that we construct for KP‐I are more general, and allow degenerate configurations such as parallel or superimposed lump chains. We also construct solutions describing interactions between lump chains and individual lumps, and discuss the relationship between the solutions obtained using the reduced and regular Grammian forms.

    

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4. A study of lump-type and interaction solutions to a (3+1)-dimensional Jimbo–Miwa-like equation

   https://doi.org/https://doi.org/10.1016/j.camwa.2018.07.008  

   Batwa, Sumayah ; Ma, Wen-Xiu ( October 2018 , Computers & mathematics with applications)

   Using generalized bilinear equations, we construct a (3+1)-dimensional Jimbo–Miwa-like equation which possesses the same bilinear type as the standard (3+1)-dimensional Jimbo–Miwa equation. Classes of lump-type solutions and interaction solutions between lump-type and kink solutions to the resulting Jimbo–Miwa-like equation are generated through Maple symbolic computation. We discuss the conditions guaranteeing analyticity and positiveness of the solutions. By taking special choices of the involved parameters, 3D plots are presented to illustrate the dynamical features of the solutions. 

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5. Diversity of interaction solutions to the (2+1)-dimensional Ito equation

   Ma, Wen-Xiu ; Yong, Xuelin ; Zhang, Hai-Qiang ( January 2018 , Computers & mathematics with applications)

   We aim to show the diversity of interaction solutions to the (2+1)-dimensional Ito equation, based on its Hirota bilinear form. The proof is given through Maple symbolic computations. An interesting characteristic in the resulting interaction solutions is the involvement of an arbitrary function. Special cases lead to lump solutions, lump-soliton solutions and lump-kink solutions. Two illustrative examples of the resulting solutions are displayed by three-dimensional plots and contour plots. 

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