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1. Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation

   Yang, Jin-Yun ; Ma, Wen-Xiu ; Qin, Zhenyun ( September 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 hyperbolic-cosine (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. 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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3. 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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4. 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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5. Lump solutions to a (2+1)-dimensional fifth-order KdV-like equation

   Batwa, Sumayah ; Ma, Wen-Xiu ( July 2018 , Advances in Mathematical Physics (Print))

   A (2+1)-dimensional fifth-order KdV-like equation is introduced through a generalized bilinear equation with the prime number . The new equation possesses the same bilinear form as the standard (2+1)-dimensional fifth-order KdV equation. By Maple symbolic computation, classes of lump solutions are constructed from a search for quadratic function solutions to the corresponding generalized bilinear equation. We get a set of free parameters in the resulting lump solutions, of which we can get a nonzero determinant condition ensuring analyticity and rational localization of the solutions. Particular classes of lump solutions with special choices of the free parameters are generated and plotted as illustrative examples. 

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