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Computing Multi-Lumps in Nonlinearity-Managed Spatial-Symmetric Dispersive Framework
Sudhir Singh, Tripathi P, Manikandan K, Sakkaravarthi K
https://arxiv.org/abs/2506.23391

Computing Multi-Lumps in Nonlinearity-Managed Spatial-Symmetric Dispersive Framework
We investigate the dynamics of multi-lump waves in a generalized spatial symmetric higher-dimensional dispersive water wave model using an analytical approach. This involves the construction of explicit solutions using Hirota's bilinear method and generalized polynomial expansions. The dynamical study shows that the multi-lump waves are non-interacting and reveal different geometrical patterns.

A Search Method for Hirota Bilinear Systems of Nonlinear Evolution Equations
I. Albazlamit, L. Al Sakkaf, U. Al Khawaja
https://arxiv.org/abs/2508.15590 https://

A Search Method for Hirota Bilinear Systems of Nonlinear Evolution Equations
We present a systematic search method for finding Hirota bilinear systems of nonlinear evolution equations, with emphasis on the nonlinear Schrödinger equation (NLSE). Using a known exact solution, couplings between the different terms of the differential equation are identified, which are then used to derive the bilinear system. We show that a nonlinear evolution equation may have many solution-dependent Hirota bilinear systems. Nonetheless, all solution members of a certain solution class ar…