Dark parameterization approach to Ito equation

TL;DR

This paper introduces a dark parameterization method to generate novel coupled Ito systems, constructs exact traveling wave solutions, and explores symmetry reductions, expanding the solution space of the Ito equation.

Contribution

The paper presents a new dark parameterization approach to coupled Ito systems and derives exact solutions and symmetry reductions, enhancing understanding of the Ito equation's solution structure.

Findings

Constructed novel traveling wave solutions.

Developed new coupled Ito systems via dark parameterization.

Analyzed symmetry reductions using Lie point symmetry theory.

Abstract

The novel coupling Ito systems are obtained with the dark parameterization approach. By solving the coupling equations, the traveling wave solutions are constructed with the mapping and deformation method. Some novel types of exact solutions are constructed with the solutions and symmetries of the usual Ito equation. In the meanwhile, the similarity reduction solutions of the model are also studied with the Lie point symmetry theory.