Work

On the Invariant Subspace Method for Nonlinear Second-Order Evolution Equations

Year: 2026

Type: article

Abstract: We investigate invariant finite-dimensional linear spaces for a class of nonlinear evolution equations with second-order time dependence of the type ∂ttu=−∂x(A(x,u)u)+∂xx(B(x,u)u)+f(u), where the coefficients may depend nonlinearly on the solution. Using direct algebraic verification and invariant subspace reductions, we derive several exact solutions and reduce the governing equations to finite-dimensional systems of ordinary differential equations. Various examples are presented to illustrate the applicability of the method to nonlinear transport, diffusion, and reaction models.

Source: Mathematics

DOI: 10.3390/math14122155

Authors: Manal Badgaish, Lhoucine Hmidouch, Nacir Hmidouch

Institutions: Umm al-Qura University, Chouaib Doukkali University, Talladega College

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Umm Al-Qura University