Computing the Dynamics of Multi-Lumps in Nonlinearity-Managed Spatial-Symmetric Dispersive Wave Framework

TL;DR

This paper introduces a new higher-dimensional nonlinear dispersive water wave model, constructs explicit multi-lump solutions analytically, and analyzes their non-interacting dynamics and geometrical patterns.

Contribution

It presents a novel (3+1)-dimensional spatial-symmetric nonlinear model and systematically derives explicit multi-lump solutions using Hirota's method.

Findings

Multi-lump waves are non-interacting.

Solutions exhibit diverse geometrical patterns.

The model enhances understanding of localized wave dynamics.

Abstract

We investigate the dynamics of multi-lump waves in a new version of a generalized spatial-symmetric higher-dimensional nonlinear dispersive water wave model using an analytical approach. This involves the proposition of a new spatial-symmetric nonlinear model in (3+1)-dimensions and the construction of its explicit solutions for multi-lump waves through a systematic analytical framework by employing Hirota's bilinear method and generalized polynomial expansions. Analyzing the resultant explicit solutions in terms of their dynamical characteristics reveals that the obtained multi-lump waves are non-interacting and exhibit different geometrical patterns. The observed results demonstrate the significance of new higher-dimensional nonlinear dispersive models in enhancing our understanding of the dynamics of various types of localized waves.