相关论文: On elliptic solutions of nonlinear ordinary differ…
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the generalized Brethenton equation are given.
Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational,…
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 determine all cases when there exists a meromorphic solution of the third order ODE describing traveling waves solutions of the Kuramoto-Sivashinsky equation. It turns out that there are no other meromorphic solutions besides those…
The Fisher-KPP equation with general nonlinear diffusion and arbitrary kinetic orders in the reaction terms is considered. The existence of oscillatory travelling wave solutions is proved for this model. Conditions for the existence of such…
A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a…
wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.
The variable separated ODE method is extended by choosing the additional variable separated equation as the general elliptic equation. More exact traveling wave solutions of nonlinear equations are obtained by using the method of comparison…
In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
Using the rudiments of pde jets theory in a nonstandard setting, we first deepen and extend previous nonstandard existence results for generalized solutions of linear differential equations and second extend the previous results for linear…
We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher…
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…
Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
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 analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel…
An approach is proposed to obtain some exact explicit solutions in terms of the Weierstrass' elliptic function $\wp$ to a generalized Benjamin-Bona-Mahony (BBM) equation. Conditions for periodic and solitary wave like solutions can be…
The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schr\"{o}dinger equation governing the propagation of pulses in optical fibers including the effects of…