Related papers: A remark on a variable-coefficient Bernoulli equat…
In this work, a new approach has been developed to obtain numerical solution of linear Volterra type integral equations by obtaining asymptotic approximation to solutions. Using the classical Bernoulli polynomials, a set of orthonormal…
In this paper, we study a compound Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. A class of solitary wave solutions is obtained by means of a series expansion.
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…
The modified method of simplest equation is applied to the extended Korteweg - de Vries equation and to generalized Camassa - Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained.…
Bernoulli's free boundary problem is an overdetermined problem in which one seeks an annular domain such that the capacitary potential satisfies an extra boundary condition. There exist two different types of solutions called elliptic and…
In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…
In this work, we study the Benjamin-Bona-Mahony like equations with a fully nonlinear dispersive term by means of the factorization technique. In this way we find the travelling wave solutions of this equation in terms of the Weierstrass…
We consider the periodic solutions of a semilinear variable coefficient wave equation arising from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. The variable coefficient…
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…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
Using an abstract scheme of monotone semiflows, the existence of bistable traveling wave solutions of a competitive recursion system with Ricker nonlinearity is established. The traveling wave solutions formulate the strong inter-specific…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
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 prove the existence of weak solutions for the one obstacle problem associated with a class of quasilinear wave equations in one space dimension, extending previous results obtained in the linear case, and we also address the two…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…
By a bifurcation argument we prove that the capillary-gravity Whitham equation features asymmetrical periodic travelling wave solution of arbitrarily small amplitude. Such waves exist only in the weak surface tension regime…