Self-controlled wave solutions to the Tzitzeica-type nonlinear models in mathematical physics

Abstract

Quantum field theory and solid-state physics phenomena are interpreted using the Tzitzeica-Dodd-Bullough model and nonlinear optics and electromagnetic waves are studied through the Dodd-Bullough-Mikhailov equation. The nonlinear Cahn-Allen model is important for describing the evolution of non-conserved order fields during anti-period sphere coarsening and the phase separation reaction–diffusion processes in multicomponent alloy structures. In this article, we have assessed the advanced and broad-spectrum solitary wave solutions to the stated models and studied the effects of wave speed as well as physical coordinates on the wave profiles and affirmed that waveform varies with the change of the free parameters associated to them. The soliton solutions are extracted by balancing the exponents of the highest-order linear and nonlinear terms. To thoroughly analyze the wave characteristic of the closed-form solutions, different standard wave profiles including kink, bell-shaped soliton, anti-peakon, periodic, quasi-periodic, complex singular, and several general solitons are depicted. Both Painlevé and traveling wave transformation play important roles in converting the equations into nonlinear differential equations. The solutions formulated in this probe are further generic, wide-spectral and some are distinctive which have not been established in the former studies.

Keywords

• The CA equation
• The TDB equation
• The DBM equations
• The EMSE method
• Solitary wave solutions