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Lump solutions to the (2+1)-dimensional shallow water wave equation

Ma Hong-Cai (Donghua University, Department of Applied Mathematics, Shanghai, China)
Ni Ke (Donghua University, Department of Applied Mathematics, Shanghai, China)
Deng Aiping (Donghua University, Department of Applied Mathematics, Shanghai, China)

Through symbolic computation with MAPLE, a class of lump solutions to the (2+1)-D shallow water wave equation is presented, making use of its Hirota bi-linear form. The resulting lump solutions contain six free parameters, two of which are due to the translation invariance of the (2+1)-D shallow water wave equation and the other four of which satisfy a non-zero determinant condition guaranteeing analyticity and rational localization of the solutions.

Keywords: lump solution, Hirota bilinear, shallow water wave equation