Abstract
By using the integral bifurcation method, a generalized Tzitzéica-Dodd-Bullough-Mikhailov (TDBM) equation is studied. Under different parameters, we investigated different kinds of exact traveling wave solutions of this generalized TDBM equation. Many singular traveling wave solutions with blow-up form and broken form, such as periodic blow-up wave solutions, solitary wave solutions of blow-up form, broken solitary wave solutions, broken kink wave solutions, and some unboundary wave solutions, are obtained. In order to visually show dynamical behaviors of these exact solutions, we plot graphs of profiles for some exact solutions and discuss their dynamical properties.
Highlights
Weiguo RuiBy using the integral bifurcation method, a generalized Tzitzeica-Dodd-Bullough-Mikhailov (TDBM) equation is studied
In this paper, we consider the following nonlinear evolution equation: uxt = αemu + βenu, (1)where α, β are two non-zero real numbers and m, n are two integers
We investigated different kinds of exact traveling wave solutions of this generalized TDBM equation
Summary
By using the integral bifurcation method, a generalized Tzitzeica-Dodd-Bullough-Mikhailov (TDBM) equation is studied. We investigated different kinds of exact traveling wave solutions of this generalized TDBM equation. Many singular traveling wave solutions with blow-up form and broken form, such as periodic blow-up wave solutions, solitary wave solutions of blow-up form, broken solitary wave solutions, broken kink wave solutions, and some unboundary wave solutions, are obtained. In order to visually show dynamical behaviors of these exact solutions, we plot graphs of profiles for some exact solutions and discuss their dynamical properties
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