相关论文: Generalized Nonlinear Equation and Solutions for F…

This paper is concerned with the final value problem for a system of nonlinear wave equations. The main issue is to solve the problem for the case where the nonlinearity is of a long range type. By assuming that the solution is spherically…

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.…

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of…

New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…

A fifth--order nonlinear partial differential equation for the description of nonlinear waves in a liquid with gas bubbles is considered. Special solutions of this equation are studied. Some elliptic and simple periodic traveling waves…

We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…

We study the general properties of spectral curves associated to doubly-periodic solutions of Korteweg-deVries, sine-Gordon, Non-linear Schr\"odinger and 1D Toda equations, and construct examples of arbitrary genus.

In this paper we analyze the interaction of an incompressible, generalized Newtonian fluid with a linearly elastic Koiter shell whose motion is restricted to transverse displacements. The middle surface of the shell constitutes the…

In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…

In this paper, we study the existence of rotating and traveling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation. The solutions are obtained by maximization of the energy over the set of rearrangements of a fixed…

Derivation of an exact, general solution to Newell-Whitehead-Segel transient, nonlinear partial differential equation is provided for one to three dimensional cases, also, arbitrary power of nonlinearity.

In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where…

We introduce a generalized similarity analysis which grants a qualitative description of the localised solutions of any nonlinear differential equation. This procedure provides relations between amplitude, width, and velocity of the…

We study the existence of traveling wave solutions to a unidirectional shallow water model which incorporates the full linear dispersion relation for both gravitational and capillary restoring forces. Using functional analytic techniques,…

In this paper we review the physical relevance of a Korteweg-de Vries (KdV) equation with higher-order dispersion terms which is used in the applied sciences and engineering. We also present exact traveling wave solutions to this…

In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…

Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional case. Nonlinear evolution equation is given for description of long nonlinear pressure waves. It is shown that in the general case the equation is…

We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…

We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…

Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently…