Mechanism investigations on certain unbounded/bounded breather molecules and transformed molecular waves for an extended (3+1)-dimensional Jimbo–Miwa equation in fluid mechanics

Abstract

In this paper, we present mechanistic investigations on certain bounded/unbounded breather molecules and transformed molecular wave formations through systematic analysis for an extended (3+1)-dimensional Jimbo–Miwa equation in fluid dynamics. Through characteristic lines analysis, we establish transformed wave solutions bifurcating from breather modes under critical state transition conditions. Such solutions demonstrate temporally evolving characteristics manifested as dynamic amplitude modulations and parametric waveform deformations. Moreover, we systematically investigate breather or transformed molecular wave complexes as collisionless structures, where the fundamental constituents are identified as individual breather waves and novel transformed wave counterparts. Unbounded or bounded molecular wave complexes, comprising identical or distinct constituent components, maintain fixed phase-locked separation distances while demonstrating propagation stability governed by nonlinear coupling constraints. These findings establish a potential theoretical framework for experimental studies in fluid dynamics, while also offering novel perspectives on the behavior of molecular waves in broader nonlinear physical systems.