<p>We aim to investigate lump waves arising from the combined effects of nonlinearity and dispersion in a newly proposed (2+1)-dimensional spatially symmetric generalized Korteweg-de Vries model. Using the bilinear method, we employ a practical ansatz based on quadratic function solutions to construct lump waves through symbolic computation in Maple. The nonlinear and dispersive terms in the model are utilized to control the characteristics of the resulting lump waves. The stationary points of these waves lie along a straight line in the spatial plane, with coordinates that vary linearly in time. The corresponding optimal values are explicitly derived and found to be time-independent.</p>

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Studying lump waves in a (2+1)-dimensional spatially symmetric generalized Korteweg-de Vries model

  • Wen-Xiu Ma,
  • Sumayah Batwa

摘要

We aim to investigate lump waves arising from the combined effects of nonlinearity and dispersion in a newly proposed (2+1)-dimensional spatially symmetric generalized Korteweg-de Vries model. Using the bilinear method, we employ a practical ansatz based on quadratic function solutions to construct lump waves through symbolic computation in Maple. The nonlinear and dispersive terms in the model are utilized to control the characteristics of the resulting lump waves. The stationary points of these waves lie along a straight line in the spatial plane, with coordinates that vary linearly in time. The corresponding optimal values are explicitly derived and found to be time-independent.