ABSTRACT Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modif...

This article concerns the traveling wave solutions of nonlocal delay reaction-diffusion equations without local quasimonotonicity. The existence of traveling wave solutions is obtained by constructing upper-lower solutions and passing to a limit function. The nonexistence of traveling wave solutions is also established by the theory of asymptotic spreading. The results are applied to a food lim...

We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R(4) and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R...

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c(*) such that for each wave speed c ≤ c(*), there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic ...

In this paper, we employ the modified simple equation method to find the exact traveling wave solutions involving parameters of nonlinear evolution equations via the (1+1)dimensional generalized shallow water-wave equation and the(2+1)-dimensional KdV-Burgers equation. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave sol...

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the ( G′ G ) -expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic so...

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection–reaction–diffusion systems. Under certain conditions, we prove that there exists a maximal wave speed c∗ such that for each wave speed c ≤ c∗, there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system. It is s...

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 ...

By using the bifurcation theory of dynamical systems to study the dynamical behavior of the Green–Naghdi equations, the existence of solitary wave solutions along with smooth periodic traveling wave solutions is obtained. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact and explicit parametric rep...

This paper is concerned with the extension of the concepts and theories of traveling wave solutions of time and space periodic monostable equations to time recurrent and space periodic ones. It first introduces the concept of generalized traveling wave solutions of time recurrent and space periodic monostable equations, which extends the concept of periodic traveling wave solutions of time and ...