Related papers: Exact Travelling Wave Solutions of Some Nonlinear …
Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method, which is applicable more generally to other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE system…
A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the…
The family of fifth order nonlinear evolution equations is studied. Some traveling wave elliptic solutions are found. The classification of these exact solutions is given.
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which…
We consider quasi-stationary (travelling wave type) solutions to a general nonlinear reaction-convection-diffusion equation with arbitrary, autonomous coefficients. The second order nonlinear equation describing one dimensional travelling…
In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with a nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to…
A method to construct the exact solution of the PDE is presents, which combines the two kind methods(the nonlinear transformation and RQ(Reduction the PDE to a Quadrature problem) method).The nonlinear diffusion equation is chosen to…
This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…
Exactly solvable variable parametric Burgers type equations in one-dimension are introduced, and two different approaches for solving the corresponding initial value problems are given. The first one is using the relationship between the…
We obtain the exact analytical traveling wave solutions of the Kolmogorov-Petrovskii-Piskunov equation with the reaction term belonging to the class of functions, which includes that of the (generalized) Fisher equation, for the particular…
In this article, we present a comprehensive analytical study to obtain the exact traveling wave solutions to a new formed model of the (2+1)-dimensional BKP equation. We construct exact solutions of the considered model using a recently…
A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…
A Lax pair consisting of the Forsyth-Hopf-Cole transformation and a linear differential (in time) - difference (in continuous space) equation generates the whole hierarchy of the Burgers equation and admits exact moving front solutions.…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
We establish a connection between the general equations of nonlinear elastodynamics and the nonlinear ordinary differential equation of Pinney [Proc. Amer. Math. Soc. 1 (1950) 681]. As a starting point, we use the exact travelling wave…
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and…
We introduce a model for nonlinear viscoelastic solids where traveling shear waves with compact support are possible. We obtain an exact compact solution. We also derive a new Burger's type evolution equation associated with the introduced…
We emphasize that construction of travelling wave solutions for partial differential equations is a problem of considerable interest and thus introduce a simple algebraic method to generate such solutions for equations in the Burgers…
We present a short review of the evolution of the methodology of the Method of simplest equation for obtaining exact particular solutions of nonlinear partial differential equations (NPDEs) and the recent extension of a version of this…
The generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented. The exact solutions of NDE systems describing the evolution of two interacting populations in two…