In this research work, we successfully construct various kinds of exact traveling wave solutions such as trigonometric like, singular and periodic well hyperbolic to the (2+1)-dimensional Chiral nonlinear Schröginger equation (CNLSE) which is used a governing discuss in quantum field theory. The mechanisms are obtain these extended rational sine-cosine/sinh-cosh constraint conditions for existe...

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...

In this article we apply the modified extended tanh-function method to find the exact traveling wave solutions of the generalized KdV-mKdV equation with any order nonlinear terms. This method presents a wider applicability for handling many other nonlinear evolution equations in mathematical physics.

In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein–Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect. By using this method, we obtain abundant new types of exact traveling wave solutions.

The Fibonacci secant function is constructed in this paper. Fibonacci tan-sec method is presented to search for the exact traveling wave solutions of nonlinear differentialdifference equations (DDEs). This method is essentially equivalent to the classical hyperbolic method. The discrete mKdV lattice and some other lattice equations are chosen to illustrate the efficiency and effectiveness of th...

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, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (fpdes) in the sense of modified riemann-liouville derivative. with the aid of symbolic computation, we choose the space-time fractional zakharov-kuznetsov-benjamin-bona-mahony (zkbbm) equation in mathematical physics with a source to illustrate the validity a...

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...