Dynamical Behavior and Nonlinear Wave Structures of a (3+1)‐Dimensional Generalized Ito Equation

Abstract

This study describes a novel connection between the algebraic integrable structure and the geometric dynamical behavior of the ‐dimensional generalized Ito equation. By considering different types of real eigenvalues, we construct Wronskian determinant type analytic solutions that include rational, positon, negaton and soliton solutions. The dynamics of the equation are further explored through the analysis of lower‐order Wronskian solutions. We further establish a new bilinear Bäcklund transformation that provides new exact solutions, illustrated through exponential and rational examples. Additionally, for identifying equilibrium points and their stability, we reduce the equation to its associated nonlinear ordinary differential equation and perform phase‐plane analysis to examine the dynamical behavior and key trajectories of the system. Moreover, by formulating traveling wave solutions based on the total energy of the system, we explore the Hamiltonian function in a conservative framework, offering insight into the geometric structure of the dynamics.